From 08f852b0942090d098b36ab6c8a6e17c8e9753cb Mon Sep 17 00:00:00 2001 From: Tournesol02 Date: Thu, 7 May 2026 23:39:00 +0200 Subject: [PATCH] Orthographie bien faite --- latex/Illustrations/NouveauxImages/Q16.png | Bin 0 -> 11098 bytes latex/Illustrations/NouveauxImages/Q18.png | Bin 0 -> 11699 bytes latex/Illustrations/NouveauxImages/Q19.png | Bin 0 -> 12118 bytes latex/Illustrations/NouveauxImages/Q_20.png | Bin 0 -> 15253 bytes latex/Questions/Q10.tex | 4 +- latex/Questions/Q13.tex | 2 +- latex/Questions/Q14.tex | 6 +- latex/Questions/Q15.tex | 12 +- latex/Questions/Q16.tex | 2 +- latex/Questions/Q17.log | 12 +- latex/Questions/Q17.tex | 2 +- latex/Questions/Q19.tex | 16 +- latex/Questions/Q2.tex | 207 +- latex/Questions/Q20.tex | 8 +- latex/Questions/Q4.tex | 2 +- latex/Questions/Q5.tex | 3 +- latex/Questions/Q6.tex | 15 +- latex/Questions/Q9.tex | 28 +- latex/contents.log | 11111 ++++++++++++++++-- latex/contents.tex | 1 + latex/main.aux | 7 +- latex/main.log | 223 +- 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d'un boucle qui travers \begin{subfigure}{0.48\textwidth} \centering \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q10} - \caption{Système au seuil: $T_s = 0.0356s$} + \caption{Système sur le seuil: $T_s = 0.0356s$} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} \centering \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q10_diverge} - \caption{Système hors seuil: $T_s = 0.0366s$} + \caption{Système hors le seuil: $T_s = 0.0366s$} \end{subfigure} \end{figure} diff --git a/latex/Questions/Q13.tex b/latex/Questions/Q13.tex index 6f325a2..3b06b04 100644 --- a/latex/Questions/Q13.tex +++ b/latex/Questions/Q13.tex @@ -1,6 +1,6 @@ \textbf{Question 13} -Avec le même periode d'echantillonnage comme dans la section precedente: $T_e=0.0356$ notre système est rendu instable. +Avec la même periode d'echantillonnage comme dans la section precedente: $T_e=0.0356$ notre système se déstabilise. \begin{figure}[H] \centering diff --git a/latex/Questions/Q14.tex b/latex/Questions/Q14.tex index 0e2a202..864b35a 100644 --- a/latex/Questions/Q14.tex +++ b/latex/Questions/Q14.tex @@ -1,19 +1,19 @@ \textbf{Question 14} -Nous retrouvons un seuil d'echantillonnage à: $T_e = 0.0107s$. Voici les comportements du système dedans et hors seuil. +Nous retrouvons un seuil d'echantillonnage à: $T_e = 0.0107s$. Voici les comportements du système sur et hors le seuil. \begin{figure}[H] \centering \begin{subfigure}{0.48\textwidth} \centering \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q14} - \caption{Système au seuil: $T_s = 0.0107s$} + \caption{Système sur le seuil: $T_s = 0.0107s$} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} \centering \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q14_instable} - \caption{Système hors seuil: $T_s = 0.0108s$} + \caption{Système hors le seuil: $T_s = 0.0108s$} \end{subfigure} \begin{subfigure}{0.48\textwidth} \centering diff --git a/latex/Questions/Q15.tex b/latex/Questions/Q15.tex index da62997..63e9c1c 100644 --- a/latex/Questions/Q15.tex +++ b/latex/Questions/Q15.tex @@ -1,4 +1,14 @@ \textbf{Question 15} +\begin{center} +Soit $q(\zeta, t) = q_0(t)$ et $F_{ext}=-\int_0^L\Phi(\zeta)q(\zeta,t)d\zeta$ +$\Leftrightarrow F_{ext}=-\int_0^L\Phi(t)q_0(t)$\\ +Or $E\dot{x}_{2d}=-D^Tx_{1d}(t)-\Phi(L)u(t)-F_{ext}$ +$\Leftrightarrow$ +$\dot{x}_{2d}=-E^{-1}D^Tx_{1d}(t)-E^{-1}\Phi(L)u(t)+ E^{-1}\int_0^L\Phi(\zeta)d\zeta q_0(t)$\\ +D'où $\dot{x}_d(t)=Ax_d(t)+Bu(t)+ \begin{bmatrix} +0_{\rm I\!R_{_{4\times1}}} \\ E^{-1}\int_0^L\Phi(\zeta)d\zeta +\end{bmatrix}q_0(t)$ +\end{center} Après avoir calculé, nous retrouvons la matrice $B_p$ sous la forme: \begin{equation} B_p = @@ -7,7 +17,7 @@ B_p = \end{bmatrix} = \begin{bmatrix} -0 & 0 & 0 & 0 & -1 & -1 & 0 & 0 +0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \end{bmatrix}^{T} \end{equation} diff --git a/latex/Questions/Q16.tex b/latex/Questions/Q16.tex index 4310d46..d379e23 100644 --- a/latex/Questions/Q16.tex +++ b/latex/Questions/Q16.tex @@ -3,7 +3,7 @@ La Figure~\ref{fig:q16_perturbation} montre que le système ne corrige pas l'erreur due à la perturbation. \begin{figure}[H] \centering - \includegraphics[scale=0.3]{Illustrations/im3} % Remplacez par votre image + \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q16} \caption{Simulation du système avec une perturbation.} \label{fig:q16_perturbation} \end{figure} diff --git a/latex/Questions/Q17.log b/latex/Questions/Q17.log index c151b70..d3d2315 100644 --- a/latex/Questions/Q17.log +++ b/latex/Questions/Q17.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 19:39 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 23:28 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -306,7 +306,7 @@ Overfull \hbox (18.91605pt too wide) in paragraph at lines 3--5 Overfull \hbox (35.55566pt too wide) in paragraph at lines 3--5 -\OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 4[]3805$ +\OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 4\OML/cmm/m/it/10 :\/cmr/m/n/10 3805$ [] @@ -479,11 +479,11 @@ cmsy/m/n/10 ^^@ \/cmr/m/n/10 3\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n Here is how much of TeX's memory you used: - 39 strings out of 474222 - 690 string characters out of 5748733 + 41 strings out of 474222 + 746 string characters out of 5748733 1923975 words of memory out of 5000000 - 22392 multiletter control sequences out of 15000+600000 + 22394 multiletter control sequences out of 15000+600000 558377 words of font info for 37 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 23i,3n,32p,268b,133s stack positions out of 10000i,1000n,20000p,200000b,200000s + 23i,3n,32p,266b,133s stack positions out of 10000i,1000n,20000p,200000b,200000s ! ==> Fatal error occurred, no output PDF file produced! diff --git a/latex/Questions/Q17.tex b/latex/Questions/Q17.tex index 1cab950..3578c32 100644 --- a/latex/Questions/Q17.tex +++ b/latex/Questions/Q17.tex @@ -1,6 +1,6 @@ \textbf{Question 17} -À partir des huit pôles obtenus avec la commande par retour d'état de la Question 11, on ajoute un pôle supplémentaire associé à l'action intégrale $p_i = -4{,}3805$, correspondant au pôle du système le plus rapide. +À partir des huit pôles obtenus avec la commande par retour d'état de la Question 11, on ajoute un pôle supplémentaire associé à l'action intégrale $p_i = -4.3805$, correspondant au pôle du système le plus rapide. Ainsi, les pôles desirés du système augmenté sont : \begin{center} $p_{\text{des}} =$ diff --git a/latex/Questions/Q19.tex b/latex/Questions/Q19.tex index e12b8cf..3d32e16 100644 --- a/latex/Questions/Q19.tex +++ b/latex/Questions/Q19.tex @@ -1,11 +1,19 @@ \textbf{Question 19} La Figure~\ref{fig:q19_integrale} montre qu'avec l'action intégrale, la perturbation est rejetée et l'erreur en régime permanent est corrigée. - \begin{figure}[H] +\centering + \begin{subfigure}{0.48\textwidth} \centering - \includegraphics[width=0.4\textwidth]{Illustrations/Q17} % Remplacez par votre image + \includegraphics[scale=0.5]{Illustrations/NouveauxImages/Q19} + \caption{Erreur en regime permanente} + \end{subfigure} + \hfill + \begin{subfigure}{0.48\textwidth} + \centering + \includegraphics[scale=0.5]{Illustrations/NouveauxImages/Q18} + \caption{Erreur nulle en regime permanente} + \end{subfigure} \caption{Simulation du système avec correction par action intégrale.} \label{fig:q19_integrale} -\end{figure} - +\end{figure} \ No newline at end of file diff --git a/latex/Questions/Q2.tex b/latex/Questions/Q2.tex index c3a1667..049d09e 100644 --- a/latex/Questions/Q2.tex +++ b/latex/Questions/Q2.tex @@ -1,73 +1,134 @@ - -\textbf{Question 2} - -À partir des informations données dans l'exercice, on peut écrire : - -\begin{equation} -\dot{x}_1 -= -\frac{\partial^2 e_2}{\partial \zeta^2} -= -\phi(\zeta)^T \dot{x}_{1d}(t) -\end{equation} - -En multipliant les deux membres par le vecteur d'approximation $\phi(\zeta)$, on obtient : - -\begin{equation} -\phi(\zeta) -\frac{\partial^2 e_2}{\partial \zeta^2} -= -\phi(\zeta)\phi(\zeta)^T \dot{x}_{1d}(t) -\end{equation} - -En remplaçant ensuite $e_2$ par son approximation, on obtient : - -\begin{equation} -\phi(\zeta) -\frac{\partial^2}{\partial \zeta^2} -\left( -\phi(\zeta)^T e_{2d}(t) -\right) -= -\phi(\zeta)\phi(\zeta)^T \dot{x}_{1d}(t) -\end{equation} - -Comme $e_{2d}(t)$ ne dépend pas de $\zeta$, il peut être sorti de l'intégrale. En intégrant sur $[0,L]$, on obtient : -\begin{equation} -\int_0^L -\phi(\zeta)\phi(\zeta)^T -\, d\zeta \, -\dot{x}_{1d}(t) -= -\int_0^L -\phi(\zeta) -\frac{\partial^2 \phi(\zeta)^T}{\partial \zeta^2} -\, d\zeta \, -e_{2d}(t) -\end{equation} - -Après avoir fait une integration par partie: -à inserer:\\ - - - -On identifie alors les matrices $E$ et $D$. Ainsi, les deux équations d'état discrétisées s'écrivent : - -\begin{equation} -\begin{aligned} -E\dot{x}_{1d}(t) &= D e_{2d}(t),\\ -E\dot{x}_{2d}(t) &= -D^T e_{1d}(t)-\phi(L)u(t)-F_{ext}. -\end{aligned} -\end{equation} - -Enfin, on obtient : - -\begin{equation} -\boxed{ -\begin{aligned} -E\dot{x}_{1d}(t) &= D e_{2d}(t),\\ -E\dot{x}_{2d}(t) &= -D^T e_{1d}(t)-\phi(L)u(t)-F_{ext},\\ -y(t) &= -\phi(L)^T e_{2d}(t). -\end{aligned} -} -\end{equation} \ No newline at end of file +\textbf{Question 2} + +\begin{equation} +\dot{x}_1 += +\frac{\partial^2}{\partial \zeta^2} e_2(\zeta,t) +\end{equation} + +Par la méthode de discrétisation : + +\begin{equation} +\phi^T(\zeta)\dot{x}_{1d}(t) += +\frac{\partial^2 \phi^T(\zeta)}{\partial \zeta^2} e_{2d}(t) \Leftrightarrow \int_0^L \phi(\zeta)\phi^T(\zeta)\,d\zeta \; \dot{x}_{1d}(t) += +\underbrace{ +\int_0^L +\phi(\zeta) +\frac{\partial^2 \phi^T(\zeta)}{\partial \zeta^2} +\,d\zeta +e_{2d}(t) +}_{J} +\end{equation} + +Par intégration par parties deux fois : + +\begin{equation} +J += +\left[ +\phi(\zeta) +\frac{\partial \phi^T(\zeta)}{\partial \zeta} +\right]_0^L +- +\int_0^L +\frac{\partial \phi(\zeta)}{\partial \zeta} +\frac{\partial \phi^T(\zeta)}{\partial \zeta} +\,d\zeta +\end{equation} + +\begin{equation} +\begin{aligned} +J +&= +\phi(L)\frac{\partial \phi^T}{\partial \zeta}(L)e_{2d}(t) +-0 +- +\left[ +\frac{\partial \phi}{\partial \zeta}(\zeta) +\phi^T(\zeta)e_{2d}(t) +\right]_0^L ++ +\int_0^L +\frac{\partial^2 \phi}{\partial \zeta^2}(\zeta) +\phi^T(\zeta)\,d\zeta \; e_{2d}(t) +\\[0.2cm] +&= +\phi(L)\frac{\partial \phi^T}{\partial \zeta}(L)e_{2d}(t) +- +\frac{\partial \phi}{\partial \zeta}(L) +\phi^T(L)e_{2d}(t) ++ +\frac{\partial \phi}{\partial \zeta}(0) +e_{2d}(0,t) ++ +\int_0^L +\frac{\partial^2 \phi}{\partial \zeta^2}(\zeta) +\phi^T(\zeta)\,e_{2d}(t)d\zeta \; +\end{aligned} +\end{equation} + + +On a $e_2(0,t)=0 \Leftrightarrow E\dot{x}_1 = De_{2d}(t)$ + + +Comme $D = +\phi(L)\frac{d\phi^T}{d\zeta}(L) +- +\frac{d\phi}{d\zeta}(L)\phi^T(L) ++ +\int_0^L +\frac{d^2\phi}{d\zeta^2}(\zeta)\phi^T(\zeta)\,d\zeta +$. Et $(AB)^T = B^T A^T$, on a : + +\begin{equation} +-D^T = +- +\frac{d\phi}{d\zeta}(L)\phi^T(L) ++ +\phi(L)\frac{d\phi^T}{d\zeta}(L) +- +\int_0^L +\phi(\zeta) +\frac{d^2\phi^T}{d\zeta^2}(\zeta) +\,d\zeta. +\end{equation} + +\begin{equation} +E\dot{x}_{2d}(t) += +- +\int_0^L +\phi(\zeta) +\frac{d^2\phi^T}{d\zeta^2}(\zeta) +\,d\zeta \; e_{1d}(t) +- +F_{ext}. +\end{equation} + +Donc, +\begin{equation} +E\dot{x}_{2d}(t) += +-D^T e_{1d}(t) ++ +\frac{d\phi}{d\zeta}(L)e_1(L,t) +- +\phi(L)\frac{\partial e_1}{\partial \zeta}(L,t) +- +F_{ext}. +\end{equation} + +Comme $e_1(L,t)=0$, $\frac{\partial e_1}{\partial \zeta}(L,t)=u(t)$ on obtient bien : + +\begin{equation} +E\dot{x}_{2d}(t) += +-D^T e_{1d}(t) +- +\phi(L)u(t) +- +F_{ext}. +\end{equation} + diff --git a/latex/Questions/Q20.tex b/latex/Questions/Q20.tex index adc008a..3e8c9b9 100644 --- a/latex/Questions/Q20.tex +++ b/latex/Questions/Q20.tex @@ -1,3 +1,9 @@ \textbf{Question 20} -Nous avons testé avec 6 decimals, mais la valeur absolue d'un des pôles z: $|z|>1$, alors nous n'arrivons jamais à stabiliser le système. Aussi, nous considerons avec $T_s \rightarrow 0.00001$ est un temps continu, la commande n'est pas implemantable sur un controleur numérique. \ No newline at end of file +Nous avons testé avec 6 decimals, mais npous avons un pôle: $|z|>1$, alors nous n'arrivons jamais à stabiliser le système. Aussi, nous considerons avec $T_s \rightarrow 0.00001$ est un temps continu, la commande n'est pas donc implemantable sur un controleur numérique. +\begin{center} +%\begin{figure} +\includegraphics[scale=0.6]{Illustrations/NouveauxImages/Q_20} +%\caption{Valeurs propres du système avec action intégrale} +%\end{figure} +\end{center} \ No newline at end of file diff --git a/latex/Questions/Q4.tex b/latex/Questions/Q4.tex index b927508..592fffe 100644 --- a/latex/Questions/Q4.tex +++ b/latex/Questions/Q4.tex @@ -1,6 +1,6 @@ \textbf{Question 4} -Voici le lieu des racines du système en continu et en temps discret. $T_s = {0.01 ; 0.02 ; 0.04}$ avec le cercle unitaire. Comme tous nos pôles sont à $|z|=1$, nous ne pouvons pas conclure sur la stabilité ni l'instabilité. En temps continu nous avons instabilité, à cause des pôles: $Re\{\lambda\}>0$ +Voici le lieu des racines du système en continu et en temps discret. $T_s = {0.01 ; 0.02 ; 0.04}$ avec le cercle unitaire. Comme tous nos pôles sont à $|z|=1$, nous ne pouvons pas conclure sur la stabilité ni l'instabilité. En temps continu le système est instable, à cause des pôles: $Re\{\lambda\}>0$ \begin{figure}[H] \centering diff --git a/latex/Questions/Q5.tex b/latex/Questions/Q5.tex index 3b8788e..09940be 100644 --- a/latex/Questions/Q5.tex +++ b/latex/Questions/Q5.tex @@ -1,10 +1,9 @@ -\newpage \textbf{Question 5} La Figure 2 montre que la sortie $y(t)$ oscille après l’échelon, confirmant l’instabilité du système en boucle ouverte. \begin{figure}[H] \centering - \includegraphics[scale=0.3]{Illustrations/Q5stepReponse} % Remplacez par votre image + \includegraphics[scale=0.4]{Illustrations/Q5stepReponse} % Remplacez par votre image \caption{Response du système en boucle ouverte.} \end{figure} \ No newline at end of file diff --git a/latex/Questions/Q6.tex b/latex/Questions/Q6.tex index 5790287..0027c0b 100644 --- a/latex/Questions/Q6.tex +++ b/latex/Questions/Q6.tex @@ -1,4 +1,13 @@ \textbf{Question 6} - -:o - +\begin{center} +Nous savons que: $ x_1(\zeta, t) = \frac{d^2 w}{d^2\zeta}(\zeta,t)$ +$\Rightarrow w(\zeta,t)=\int\int_0^L x_1(\mu , t)d\mu $\\ +comme $x_1(\mu,t)=\Phi^T(\mu)x_{1d}(t)$\\ +d'où +\begin{equation} +w(\zeta,t) = +\begin{bmatrix} +\int\int_0^\zeta \Phi(\mu)d\mu & 0_{{\rm I\!R}_{1\times4}} +\end{bmatrix}x_d(t) +\end{equation} +\end{center} \ No newline at end of file diff --git a/latex/Questions/Q9.tex b/latex/Questions/Q9.tex index c413731..a9f5789 100644 --- a/latex/Questions/Q9.tex +++ b/latex/Questions/Q9.tex @@ -2,33 +2,33 @@ \textbf{Question 9} La Figure~\ref{fig:q9_eigenvalues} compare les valeurs propres du système en boucle fermée en temps continu avec celles obtenues après discrétisation par ZOH, pour les trois périodes d'échantillonnage proposées: $T_e = \{0.01s ; 0.02s ; 0.04s\}$. - \begin{figure}[H] -\centering + \centering \begin{subfigure}{0.48\textwidth} - \centering + \centering \includegraphics[scale=0.3]{Illustrations/Q9continu} - \caption{Valeurs propres en temps continu.} + \caption{Valeurs propres en temps continu.} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} - \centering - \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q9_TE001} - \caption{$T_s = 0.01\,\mathrm{s}$.} + \centering + \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q9_TE001} + \caption{$T_s = 0.01\,\mathrm{s}$.} \end{subfigure} - \begin{subfigure}{0.48\textwidth} - \centering + \begin{subfigure}{0.48\textwidth} + \centering \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q9_TE002} - \caption{$T_s = 0.02\,\mathrm{s}$.} + \caption{$T_s = 0.02\,\mathrm{s}$.} \end{subfigure} \hfill \begin{subfigure}{0.48\textwidth} - \centering - \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q9_TE004} - \caption{$T_s = 0.04\,\mathrm{s}$.} + \centering + \includegraphics[scale=0.4]{Illustrations/NouveauxImages/Q9_TE004} + \caption{$T_s = 0.04\,\mathrm{s}$.} \end{subfigure} + \caption{Valeurs propres dans le cas d'un retour de sortie} \label{fig:q9_eigenvalues} \end{figure} -Comme nous pouvons voir, les pôles du système discret restent à l'interieur du cercle unitaire, mais dès que nous passons à $T_e=0.04s$ ça rend le système instable avec un pôle hors le cercle. +Comme nous pouvons voir, les pôles du système discret restent à l'interieur du cercle unitaire, mais prendre $T_e=0.04s$ rend le système instable avec un pôle hors du cercle. diff --git a/latex/contents.log b/latex/contents.log index bc88fc5..cb3c2ef 100644 --- a/latex/contents.log +++ b/latex/contents.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 28 APR 2026 16:15 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 23:38 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -7,8 +7,8 @@ entering extended mode LaTeX2e <2023-11-01> patch level 1 L3 programming layer <2024-01-22> ! 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Corrupted NFSS tables. -wrong@fontshape ...message {Corrupted NFSS tables} - error@fontshape else let f... -l.5 \section{Dynamique du systè - me avec équations differentielles partielles} -This error message was generated by an \errmessage -command, so I can't give any explicit help. -Pretend that you're Hercule Poirot: Examine all clues, -and deduce the truth by order and method. - - -LaTeX Font Warning: Font shape `/cmr/m/n' undefined -(Font) using `OT1/cmr/m/n' instead on input line 5. - -Missing character: There is no m in font nullfont! -Missing character: There is no e in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no P in font nullfont! +(./Questions/Q1.tex +Overfull \hbox (29.44446pt too wide) in paragraph at lines 6--1 +[]\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 6--1 +\/cmr/m/n/10 ^^Re + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.2 \textbf{Question 1} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (64.64003pt too wide) in paragraph at lines 2--3 +[]\OT1/cmr/bx/n/10 Question + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 2--3 +\OT1/cmr/bx/n/10 1 + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.4 A + partir des equations diferentielles partielles nous avons retrouvé l'... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no A in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no a in font nullfont! @@ -147,7 +158,6 @@ Missing character: There is no s in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no f in font nullfont! -Missing character: There is no f in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! @@ -169,53 +179,44 @@ Missing character: There is no l in font nullfont! Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! -! Undefined control sequence. -l.6 \subsection - {Espace d'état} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - -Missing character: There is no E in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! -Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! -Missing character: There is no c in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no d in font nullfont! -Missing character: There is no ' in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no a in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no L in font nullfont! -Missing character: There is no ' in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no p in font nullfont! -Missing character: There is no a in font nullfont! -Missing character: There is no c in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no d in font nullfont! -Missing character: There is no ' in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no a in font nullfont! -Missing character: There is no t in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! Missing character: There is no s in font nullfont! +Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no v in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no s in font nullfont! -Missing character: There is no l in font nullfont! -Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no r in font nullfont! @@ -223,51 +224,24 @@ Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no : in font nullfont! -Overfull \hbox (20.0pt too wide) in paragraph at lines 5--8 +Overfull \hbox (20.0pt too wide) in paragraph at lines 4--5 [] [] -Overfull \hbox (9.44446pt too wide) in paragraph at lines 5--8 -\/cmr/m/n/10 ^^Re - [] - - -Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--8 +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--5 \/cmr/m/n/10 ^^Se [] -Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--8 +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--5 \/cmr/m/n/10 ^^Se [] - -Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--8 -\/cmr/m/n/10 ^^Se - [] - - -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.9 \begin{center} - -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - - -Overfull \hbox (20.0pt too wide) in paragraph at lines 9--9 -[] - [] - LaTeX Font Info: External font `cmex10' loaded for size -(Font) <7> on input line 10. +(Font) <7> on input line 5. LaTeX Font Info: External font `cmex10' loaded for size -(Font) <5> on input line 10. +(Font) <5> on input line 5. ! LaTeX Error: Environment bmatrix undefined. @@ -275,38 +249,70 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.11 ...rtial^2}{\partial \zeta ^2}\begin{bmatrix} - +l.8 \begin{bmatrix} + Your command was ignored. Type I to replace it with another command, or to continue without it. -! LaTeX Error: \begin{equation} on input line 10 ended by \end{bmatrix}. +! LaTeX Error: \begin{equation} on input line 5 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.13 \end{bmatrix} +l.11 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. -Overfull \hbox (196.54666pt too wide) detected at line 15 -\OML/cmm/m/it/10 ^^Z\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[](\OML/cmm -/m/it/10 ^^P; t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@[]\OML/cmm/m/it/10 EI\/cmr/ -m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[](\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/1 -0 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 q\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; -t\/cmr/m/n/10 ) - [] +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.14 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.15 0 & + 1 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.16 -1 & + 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. -Overfull \hbox (18.51382pt too wide) in paragraph at lines 15--17 - $\OML/cmm/m/it/10 E \/cmr/m/n/10 =$ - [] +! LaTeX Error: \begin{equation} on input line 5 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. ! LaTeX Error: Environment bmatrix undefined. @@ -321,511 +327,14 @@ Your command was ignored. Type I to replace it with another command, or to continue without it. -! Misplaced alignment tab character &. -l.19 13/35 & - 9/70 & 11/210 &-13/420 \\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. -! Misplaced alignment tab character &. -l.19 13/35 & 9/70 & - 11/210 &-13/420 \\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -! Misplaced alignment tab character &. -l.19 13/35 & 9/70 & 11/210 & - -13/420 \\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - - -! LaTeX Error: There's no line here to end. +! LaTeX Error: \begin{equation} on input line 5 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.19 13/35 & 9/70 & 11/210 &-13/420 \\ - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Missing $ inserted. - - $ -l.19 13/35 & 9/70 & 11/210 &-13/420 \\ - -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - -! Missing } inserted. - - } -l.19 13/35 & 9/70 & 11/210 &-13/420 \\ - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Missing \endgroup inserted. - - \endgroup -l.19 13/35 & 9/70 & 11/210 &-13/420 \\ - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Display math should end with $$. - - \tex_par:D -l.19 13/35 & 9/70 & 11/210 &-13/420 \\ - -The `$' that I just saw supposedly matches a previous `$$'. -So I shall assume that you typed `$$' both times. - - -Overfull \hbox (112.77812pt too wide) detected at line 19 -\/cmr/m/n/10 13\OML/cmm/m/it/10 =\/cmr/m/n/10 359\OML/cmm/m/it/10 =\/cmr/m/n/10 - 7011\OML/cmm/m/it/10 =\/cmr/m/n/10 210 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 13\OM -L/cmm/m/it/10 =\/cmr/m/n/10 420[] - [] - -! Extra }, or forgotten \endgroup. -\par ...m \@noitemerr {\@@par }\fi \else {\@@par } - \fi -l.19 13/35 & 9/70 & 11/210 &-13/420 \\ - -I've deleted a group-closing symbol because it seems to be -spurious, as in `$x}$'. But perhaps the } is legitimate and -you forgot something else, as in `\hbox{$x}'. In such cases -the way to recover is to insert both the forgotten and the -deleted material, e.g., by typing `I$}'. - -Missing character: There is no 9 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 7 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.20 9/70 & - 13/35 & 13/420 & -11/210\\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no 1 in font nullfont! -Missing character: There is no 3 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 3 in font nullfont! -Missing character: There is no 5 in font nullfont! -! Misplaced alignment tab character &. -l.20 9/70 & 13/35 & - 13/420 & -11/210\\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no 1 in font nullfont! -Missing character: There is no 3 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 4 in font nullfont! -Missing character: There is no 2 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.20 9/70 & 13/35 & 13/420 & - -11/210\\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no - in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 2 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 0 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 2 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.21 11/210 & - 13/420 & 1/105 & -1/140\\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no 1 in font nullfont! -Missing character: There is no 3 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 4 in font nullfont! -Missing character: There is no 2 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.21 11/210 & 13/420 & - 1/105 & -1/140\\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 0 in font nullfont! -Missing character: There is no 5 in font nullfont! -! Misplaced alignment tab character &. -l.21 11/210 & 13/420 & 1/105 & - -1/140\\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no - in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 4 in font nullfont! -Missing character: There is no 0 in font nullfont! -Missing character: There is no - in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 3 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 4 in font nullfont! -Missing character: There is no 2 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.22 -13/420 & - -11/210 & -1/140 & 1/105 -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no - in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 2 in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.22 -13/420 & -11/210 & - -1/140 & 1/105 -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no - in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 4 in font nullfont! -Missing character: There is no 0 in font nullfont! -! Misplaced alignment tab character &. -l.22 -13/420 & -11/210 & -1/140 & - 1/105 -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -Missing character: There is no 1 in font nullfont! -Missing character: There is no / in font nullfont! -Missing character: There is no 1 in font nullfont! -Missing character: There is no 0 in font nullfont! -Missing character: There is no 5 in font nullfont! - -! LaTeX Error: \begin{center} on input line 9 ended by \end{bmatrix}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.23 \end{bmatrix} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - - -! LaTeX Error: Bad math environment delimiter. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.24 \] - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - - -Overfull \hbox (187.56427pt too wide) detected at line 28 -\OML/cmm/m/it/10 x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = [](\O -ML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) \OML/cmm/m/it/10 x[]\/cmr/m/n/10 (\OML/cmm/ -m/it/10 ^^P; t\/cmr/m/n/10 ) = \OML/cmm/m/it/10 ^^Z\/cmr/m/n/10 (\OML/cmm/m/it/ -10 ^^P\/cmr/m/n/10 )[](\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) - [] - - -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.30 \begin{equation} - -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - - -Overfull \hbox (20.0pt too wide) in paragraph at lines 30--30 -[] - [] - - -Overfull \hbox (198.40678pt too wide) detected at line 33 -\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = \OML/ -cmm/m/it/10 EI\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/10 -x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) \OML/cmm/m/it/10 e[]\/cm -r/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = []\OML/cmm/m/it/10 x[]\/cmr/m -/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) - [] - - -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.35 \begin{equation} - -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - - -Overfull \hbox (20.0pt too wide) in paragraph at lines 35--35 -[] - [] - - -! LaTeX Error: Environment bmatrix undefined. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.36 \dot{x(t)}=\begin{bmatrix} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Missing $ inserted. - - $ -l.37 - -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - -! Missing \endgroup inserted. - - \endgroup -l.37 - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Display math should end with $$. - - \tex_par:D -l.37 - -The `$' that I just saw supposedly matches a previous `$$'. -So I shall assume that you typed `$$' both times. - - -Overfull \hbox (27.6597pt too wide) detected at line 37 -[] \/cmr/m/n/10 = - [] - -! Missing $ inserted. - - $ -l.38 \dot - {x_1} \\ -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - - -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.38 \dot - {x_1} \\ -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - - -! LaTeX Error: \begin{equation} on input line 35 ended by \end{bmatrix}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.40 \end{bmatrix} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Missing $ inserted. - - $ -l.40 \end{bmatrix} - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -Missing character: There is no = in font nullfont! -! Missing $ inserted. - - $ -l.41 = \frac{\partial^2}{\partial z^2} - -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - -! Missing $ inserted. - - $ -l.41 = \frac{\partial^2}{\partial z^2} - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Missing $ inserted. - - $ -l.41 = \frac{\partial^2}{\partial z^2} - -I've inserted a begin-math/end-math symbol since I think -you left one out. Proceed, with fingers crossed. - -! Extra }, or forgotten $. -\frac #1#2->{\begingroup #1\endgroup \over #2} - -l.41 = \frac{\partial^2}{\partial z^2} - -I've deleted a group-closing symbol because it seems to be -spurious, as in `$x}$'. But perhaps the } is legitimate and -you forgot something else, as in `\hbox{$x}'. In such cases -the way to recover is to insert both the forgotten and the -deleted material, e.g., by typing `I$}'. - - -! LaTeX Error: Environment bmatrix undefined. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.42 \begin{bmatrix} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Misplaced alignment tab character &. -l.43 0 & - 1 \\ -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - -! Misplaced alignment tab character &. -l.44 -1 & - 0 -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - - -! LaTeX Error: \begin{document} ended by \end{bmatrix}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.45 \end{bmatrix} +l.21 \end{bmatrix} Your command was ignored. Type I to replace it with another command, @@ -838,184 +347,2386 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.46 \begin{bmatrix} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Misplaced alignment tab character &. -l.47 e_1(\zeta,t) & - e_2(\zeta ,t) -I can't figure out why you would want to use a tab mark -here. If you just want an ampersand, the remedy is -simple: Just type `I\&' now. But if some right brace -up above has ended a previous alignment prematurely, -you're probably due for more error messages, and you -might try typing `S' now just to see what is salvageable. - - -! LaTeX Error: \begin{document} ended by \end{bmatrix}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.48 \end{bmatrix} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - - -! LaTeX Error: Environment bmatrix undefined. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.50 \begin{bmatrix} +l.23 \begin{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. -! LaTeX Error: \begin{document} ended by \end{bmatrix}. +! LaTeX Error: \begin{equation} on input line 5 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.53 \end{bmatrix} +l.26 \end{bmatrix} Your command was ignored. Type I to replace it with another command, or to continue without it. -! You can't use `\eqno' in math mode. -\eqno ->\@kernel@eqno - \aftergroup \ignorespaces -l.54 \end{equation} - -Sorry, but I'm not programmed to handle this case; -I'll just pretend that you didn't ask for it. -If you're in the wrong mode, you might be able to -return to the right one by typing `I}' or `I$' or `I\par'. - -! LaTeX Error: \begin{document} ended by \end{equation}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.54 \end{equation} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Missing $ inserted. - - $ -l.54 \end{equation} - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Missing } inserted. - - } -l.54 \end{equation} - -I've inserted something that you may have forgotten. -(See the above.) -With luck, this will get me unwedged. But if you -really didn't forget anything, try typing `2' now; then -my insertion and my current dilemma will both disappear. - -! Extra \endgroup. - \endgroup - -l.54 \end{equation} - -Things are pretty mixed up, but I think the worst is over. - - -Overfull \hbox (30.2014pt too wide) in paragraph at lines 38--55 -[]$[][] +Overfull \hbox (204.9278pt too wide) detected at line 27 +[] \/cmr/m/n/10 = [][] [] = []01[] \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 10\OML/cm +m/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 )[] \OML/cmm/m/i +t/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) + 0[] \OMS/cmsy/m/ +n/10 ^^@ \OML/cmm/m/it/10 q\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) [] - -Overfull \hbox (10.2014pt too wide) in paragraph at lines 38--55 -[]$ - [] - - -Overfull \hbox (143.33615pt too wide) in paragraph at lines 38--55 -\OML/cmm/m/it/10 @[]$$[]$$$ - [] - - -! LaTeX Error: \begin{document} ended by \end{center}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.55 \end{center} - -Your command was ignored. -Type I to replace it with another command, -or to continue without it. - -! Extra \endgroup. - \endgroup - -l.55 \end{center} - -Things are pretty mixed up, but I think the worst is over. - -Missing character: There is no J in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no v in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no m in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no r in font nullfont! -Missing character: There is no e in font nullfont! +) ! Undefined control sequence. -l.58 \section - {Une autre section} +l.9 \subsection + {Discrétisation par éléments finis} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. -Missing character: There is no U in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no a in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no r in font nullfont! -Missing character: There is no e in font nullfont! +Missing character: There is no D in font nullfont! +Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! -Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +(./Questions/Q2.tex +Overfull \hbox (4.44444pt too wide) in paragraph at lines 27--2 + \/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (8.88889pt too wide) in paragraph at lines 27--2 +\/cmr/m/n/10 ^^Se^^Se + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 27--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 27--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 27--2 +\OT1/cmr/bx/n/10 2 + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.3 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--3 +[] + [] + + +Overfull \hbox (71.48676pt too wide) detected at line 7 +[] \/cmr/m/n/10 = []\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/ +cmr/m/n/10 ) + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 P + ar la méthode de discrétisation : +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no P in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 9--10 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 9--10 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 9--10 +\/cmr/m/n/10 ^^Se + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 11--11 +[] + [] + + +Overfull \hbox (368.9626pt too wide) detected at line 23 +\OML/cmm/m/it/10 ^^^[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[](\OML/c +mm/m/it/10 t\/cmr/m/n/10 ) = []\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/ +10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 , [][] \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\O +ML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/10 ^^^[]\/cmr/m/n/10 (\OML/cmm/m/ +it/10 ^^P\/cmr/m/n/10 ) \OML/cmm/m/it/10 d^^P []\/cmr/m/n/10 (\OML/cmm/m/it/10 +t\/cmr/m/n/10 ) = [] + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.25 P + ar intégration par parties deux fois : +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no P in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 25--26 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 25--26 +\/cmr/m/n/10 ^^Se + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.27 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 27--27 +[] + [] + + +Overfull \hbox (186.58586pt too wide) detected at line 39 +\OML/cmm/m/it/10 J \/cmr/m/n/10 = [][] \OMS/cmsy/m/n/10 ^^@ [][] [][] \OML/cmm/ +m/it/10 d^^P + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.41 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 41--41 +[] + [] + + +! LaTeX Error: Environment aligned undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 \begin{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.44 & + = +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.57 & + = +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 41 ended by \end{aligned}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.69 \end{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (708.21799pt too wide) detected at line 70 +\OML/cmm/m/it/10 J \/cmr/m/n/10 = \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/ +it/10 L\/cmr/m/n/10 )[](\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 e[]\/c +mr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 0 + \OMS/cmsy/m/n/10 ^^@ [][] \/cmr/m/n/10 + [][] [](\OML/cmm/m/it/10 ^^P\/cmr/m/n +/10 )\OML/cmm/m/it/10 ^^^[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 ) \OM +L/cmm/m/it/10 d^^P e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OML/cm +m/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )[](\OML/cmm/m/it/10 +L\/cmr/m/n/10 )\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 + ) \OMS/cmsy/m/n/10 ^^@ []\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cm +m/m/it/10 ^^^[]\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 e +[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + [](0)\OML/cmm/m/it/10 e[]\/c +mr/m/n/10 (0\OML/cmm/m/it/10 ; t\/cmr/m/n/10 ) + [][] [](\OML/cmm/m/it/10 ^^P\/ +cmr/m/n/10 )\OML/cmm/m/it/10 ^^^[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/1 +0 ) \OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/ +m/it/10 d^^P + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.73 O + n a $e_2(0,t)=0 \Leftrightarrow E\dot{x}_1 = De_{2d}(t)$ +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no O in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 73--74 +[] + [] + + +Overfull \hbox (40.53125pt too wide) in paragraph at lines 73--74 +\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (0\OML/cmm/m/it/10 ; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (17.77774pt too wide) in paragraph at lines 73--74 +\/cmr/m/n/10 0 \OMS/cmsy/m/n/10 , + [] + + +Overfull \hbox (28.71523pt too wide) in paragraph at lines 73--74 +\OML/cmm/m/it/10 E[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (33.25113pt too wide) in paragraph at lines 73--74 +\OML/cmm/m/it/10 De[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.76 C + omme $D = +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 76--84 +[] + [] + + +Overfull \hbox (19.11246pt too wide) in paragraph at lines 76--84 +\OML/cmm/m/it/10 D \/cmr/m/n/10 = + [] + + +Overfull \hbox (59.80368pt too wide) in paragraph at lines 76--84 +\OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )[](\OML/cmm/m +/it/10 L\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (60.57375pt too wide) in paragraph at lines 76--84 +[]\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 ^^^[]\/cmr/m/n +/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 ) + + [] + + +Overfull \hbox (79.61713pt too wide) in paragraph at lines 76--84 +[][] []\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/10 ^^^[]\/ +cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 ) \OML/cmm/m/it/10 d^^P$ + [] + + +Overfull \hbox (40.21979pt too wide) in paragraph at lines 76--84 +\/cmr/m/n/10 (\OML/cmm/m/it/10 AB\/cmr/m/n/10 )[] = + [] + + +Overfull \hbox (28.18613pt too wide) in paragraph at lines 76--84 +\OML/cmm/m/it/10 B[]A[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.85 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 85--85 +[] + [] + + +Overfull \hbox (257.78047pt too wide) detected at line 96 +\OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 D[] \/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@[]\ +/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 ^^^[]\/cmr/m/n/10 + (\OML/cmm/m/it/10 L\/cmr/m/n/10 ) + \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm +/m/it/10 L\/cmr/m/n/10 )[](\OML/cmm/m/it/10 L\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^ +@ [][] \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[](\ +OML/cmm/m/it/10 ^^P\/cmr/m/n/10 ) \OML/cmm/m/it/10 d^^P: + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.98 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 98--98 +[] + [] + + +Overfull \hbox (198.52264pt too wide) detected at line 108 +\OML/cmm/m/it/10 E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/ +m/n/10 ^^@ [][] \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n +/10 )[](\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 ) \OML/cmm/m/it/10 d^^P e[]\/cmr/m/n/1 +0 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 F[]: + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.110 D + onc, +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no D in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no , in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 110--111 +[] + [] + + +Overfull \hbox (259.2802pt too wide) detected at line 121 +\OML/cmm/m/it/10 E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/ +m/n/10 ^^@\OML/cmm/m/it/10 D[]e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + + [](\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cm +m/m/it/10 L; t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 ^^^\/cmr/m/n +/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )[](\OML/cmm/m/it/10 L; t\/cmr/m/n/10 ) \OM +S/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 F[]: + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.123 C + omme $e_1(L,t)=0$, $\frac{\partial e_1}{\partial \zeta}(L,t)=u(t)$ on... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 123--124 +[] + [] + + +Overfull \hbox (42.3368pt too wide) in paragraph at lines 123--124 +\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 L; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 123--124 +\/cmr/m/n/10 0$ + [] + + +Overfull \hbox (47.99239pt too wide) in paragraph at lines 123--124 +[]\/cmr/m/n/10 (\OML/cmm/m/it/10 L; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (17.1135pt too wide) in paragraph at lines 123--124 +\OML/cmm/m/it/10 u\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.125 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 125--125 +[] + [] + + +Overfull \hbox (168.64215pt too wide) detected at line 133 +\OML/cmm/m/it/10 E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/ +m/n/10 ^^@\OML/cmm/m/it/10 D[]e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr +/m/n/10 )\OML/cmm/m/it/10 u\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/ +cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 F[]: + [] + +) (./Questions/Q3.tex + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.1 \textbf{Question 3} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (64.64003pt too wide) in paragraph at lines 1--2 +[]\OT1/cmr/bx/n/10 Question + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 1--2 +\OT1/cmr/bx/n/10 3 + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.3 L + e système devient avec $\rho = EI = 1$ et $q(\zeta,t)=0$ : +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no L in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--4 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (15.72566pt too wide) in paragraph at lines 3--4 +\OML/cmm/m/it/10 ^^Z \/cmr/m/n/10 = + [] + + +Overfull \hbox (23.69437pt too wide) in paragraph at lines 3--4 +\OML/cmm/m/it/10 EI \/cmr/m/n/10 = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 1$ + [] + + +Overfull \hbox (36.3246pt too wide) in paragraph at lines 3--4 +\OML/cmm/m/it/10 q\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 0$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--5 +[] + [] + + +! LaTeX Error: Environment aligned undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.6 \begin{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.7 E\dot{x}_{1d}(t) & + = D x_{2d}(t),\\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 E\dot{x}_{2d}(t) & + = -D^T x_{1d}(t)-\phi(L)u(t),\\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.9 y(t) & + = -\phi(L)^T x_{2d}(t). +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 5 ended by \end{aligned}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 \end{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (324.24289pt too wide) detected at line 11 +\OML/cmm/m/it/10 E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OML/cmm/m +/it/10 Dx[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] +E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cm +m/m/it/10 D[]x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 + ^^@ \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm +/m/it/10 u\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] y +\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cmm/m +/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )[]\OML/cmm/m/it/10 x[]\ +/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 : + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.13 E + n multipliant les deux premières équations par $E^{-1}$, on obtient : +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no E in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 13--14 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 13--14 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 13--14 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (18.69446pt too wide) in paragraph at lines 13--14 +\OML/cmm/m/it/10 E[]$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.15 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 15--15 +[] + [] + + +! LaTeX Error: Environment aligned undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \begin{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.17 \dot{x}_{1d}(t) & + = E^{-1}D x_{2d}(t),\\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.18 \dot{x}_{2d}(t) & + = -E^{-1}D^T x_{1d}(t)-E^{-1}\phi(L)u(t). +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 15 ended by \end{aligned}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.19 \end{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (269.60913pt too wide) detected at line 20 +[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OML/cmm/m/it/10 E[]Dx[]\/cm +r/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; [] []\/cmr/m/n/10 +(\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 E[]D[] +x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \OML/cmm +/m/it/10 E[]^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 u +\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 : + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.22 E + t, on obtient comme valeurs de $A$, $B$ et $C$ : +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no E in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 22--23 +[] + [] + + +Overfull \hbox (7.50002pt too wide) in paragraph at lines 22--23 +\OML/cmm/m/it/10 A$ + [] + + +Overfull \hbox (8.0868pt too wide) in paragraph at lines 22--23 +\OML/cmm/m/it/10 B$ + [] + + +Overfull \hbox (7.86249pt too wide) in paragraph at lines 22--23 +\OML/cmm/m/it/10 C$ + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 24--24 +[] + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.26 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.27 0 & + E^{-1}D \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.28 -E^{-1}D^T & + 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 24 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \end{bmatrix} + = +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.30 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.31 0 & + 0 & 0 & 0 & 114 & 6 & 12 & -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.31 0 & 0 & + 0 & 0 & 114 & 6 & 12 & -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.31 0 & 0 & 0 & + 0 & 114 & 6 & 12 & -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.31 0 & 0 & 0 & 0 & + 114 & 6 & 12 & -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.31 0 & 0 & 0 & 0 & 114 & + 6 & 12 & -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.31 0 & 0 & 0 & 0 & 114 & 6 & + 12 & -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.31 0 & 0 & 0 & 0 & 114 & 6 & 12 & + -2 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & + 0 & 0 & 0 & -54 & -6 & -2 & 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & 0 & + 0 & 0 & -54 & -6 & -2 & 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & 0 & 0 & + 0 & -54 & -6 & -2 & 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & 0 & 0 & 0 & + -54 & -6 & -2 & 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & 0 & 0 & 0 & -54 & + -6 & -2 & 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & 0 & 0 & 0 & -54 & -6 & + -2 & 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.32 0 & 0 & 0 & 0 & -54 & -6 & -2 & + 4 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & + 0 & 0 & 0 & -1188 & -12 & -114 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & 0 & + 0 & 0 & -1188 & -12 & -114 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & 0 & 0 & + 0 & -1188 & -12 & -114 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & 0 & 0 & 0 & + -1188 & -12 & -114 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & 0 & 0 & 0 & -1188 & + -12 & -114 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & 0 & 0 & 0 & -1188 & -12 & + -114 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.33 0 & 0 & 0 & 0 & -1188 & -12 & -114 & + 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & + 0 & 0 & 0 & -828 & -12 & -54 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & 0 & + 0 & 0 & -828 & -12 & -54 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & 0 & 0 & + 0 & -828 & -12 & -54 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & 0 & 0 & 0 & + -828 & -12 & -54 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & 0 & 0 & 0 & -828 & + -12 & -54 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & 0 & 0 & 0 & -828 & -12 & + -54 & 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.34 0 & 0 & 0 & 0 & -828 & -12 & -54 & + 6 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & + 54 & 4 & -2 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & 54 & + 4 & -2 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & 54 & 4 & + -2 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & 54 & 4 & -2 & + 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & 54 & 4 & -2 & 0 & + 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & 54 & 4 & -2 & 0 & 0 & + 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.35 6 & 54 & 4 & -2 & 0 & 0 & 0 & + 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & + -114 & -2 & 12 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & -114 & + -2 & 12 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & -114 & -2 & + 12 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & -114 & -2 & 12 & + 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & -114 & -2 & 12 & 0 & + 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & -114 & -2 & 12 & 0 & 0 & + 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.36 -6 & -114 & -2 & 12 & 0 & 0 & 0 & + 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & + -828 & -6 & 54 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & -828 & + -6 & 54 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & -828 & -6 & + 54 & 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & -828 & -6 & 54 & + 0 & 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & -828 & -6 & 54 & 0 & + 0 & 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & -828 & -6 & 54 & 0 & 0 & + 0 & 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.37 -12 & -828 & -6 & 54 & 0 & 0 & 0 & + 0 \\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & + -1188 & -6 & 114 & 0 & 0 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & -1188 & + -6 & 114 & 0 & 0 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & -1188 & -6 & + 114 & 0 & 0 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & -1188 & -6 & 114 & + 0 & 0 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & -1188 & -6 & 114 & 0 & + 0 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & -1188 & -6 & 114 & 0 & 0 & + 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.38 -12 & -1188 & -6 & 114 & 0 & 0 & 0 & + 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 24 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.39 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (728.30418pt too wide) detected at line 40 +\OML/cmm/m/it/10 A \/cmr/m/n/10 = 0\OML/cmm/m/it/10 E[]D[] \OMS/cmsy/m/n/10 ^^ +@ \OML/cmm/m/it/10 E[]D[]\/cmr/m/n/10 0 = 0000114612 \OMS/cmsy/m/n/10 ^^@ \/cmr +/m/n/10 2[] 0000 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 54 \OMS/cmsy/m/n/10 ^^@ \/cm +r/m/n/10 6 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 24[] 0000 \OMS/cmsy/m/n/10 ^^@ \/c +mr/m/n/10 1188 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/ +m/n/10 1146[] 0000 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 828 \OMS/cmsy/m/n/10 ^^@ \ +/cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 546[] 6544 \OMS/cmsy/m/n/10 ^^ +@ \/cmr/m/n/10 20000[] \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 6 \OMS/cmsy/m/n/10 ^^ +@ \/cmr/m/n/10 114 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 2120000[] \OMS/cmsy/m/n/1 +0 ^^@ \/cmr/m/n/10 12 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 828 \OMS/cmsy/m/n/10 ^^ +@ \/cmr/m/n/10 6540000[] \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 12 \OMS/cmsy/m/n/10 + ^^@ \/cmr/m/n/10 1188 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 61140000 + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.42 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 42--42 +[] + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.44 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{equation} on input line 42 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.46 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.48 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.49 0 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.50 0 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.51 0 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.52 0 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.53 4 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.54 -16 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.55 -60 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 42 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.57 \end{bmatrix} + ^{T} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (177.66437pt too wide) detected at line 58 +\OML/cmm/m/it/10 B \/cmr/m/n/10 = 0[] \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 E[ +]\/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 L\/cmr/m/n/10 ) = 00004 \OMS/cmsy/m/n/10 ^^@ + \/cmr/m/n/10 16 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 60 \OMS/cmsy/m/n/10 ^^@ \/cm +r/m/n/10 120[] + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.62 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.63 0 & + -\Phi^{T}(L,t) +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 59 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.64 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.66 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.67 0 & + 0 & 0 & 0 & 0 & -1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.67 0 & 0 & + 0 & 0 & 0 & -1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.67 0 & 0 & 0 & + 0 & 0 & -1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.67 0 & 0 & 0 & 0 & + 0 & -1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.67 0 & 0 & 0 & 0 & 0 & + -1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.67 0 & 0 & 0 & 0 & 0 & -1 & + 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.67 0 & 0 & 0 & 0 & 0 & -1 & 0 & + 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 59 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.68 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (131.24545pt too wide) detected at line 69 + \OML/cmm/m/it/10 C \/cmr/m/n/10 = 0 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 ^^H[](\O +ML/cmm/m/it/10 L; t\/cmr/m/n/10 ) = 00000 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 100 + + [] + +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.72 \begin{equation} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 72--72 +[] + [] + +! Undefined control sequence. +l.73 \boxed + { +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: Environment aligned undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.74 \begin{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.75 \dot{x}_d(t) & + = Ax_d(t)+Bu(t),\\ +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.76 y(t) & + = Cx_d(t). +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 72 ended by \end{aligned}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.77 \end{aligned} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (168.62527pt too wide) detected at line 79 +[] + [] + +) + +! LaTeX Error: The font size command \normalsize is not defined: + there is probably something wrong with the class file. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.12 \newpage + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] (./Questions/Q4.tex + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.1 \textbf{Question 4} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (64.64003pt too wide) in paragraph at lines 1--2 +[]\OT1/cmr/bx/n/10 Question + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 1--2 +\OT1/cmr/bx/n/10 4 + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.3 V + oici le lieu des racines du système en continu et en temps discret. $T... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! 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LaTeX Error: Environment figure undefined. @@ -1023,18 +2734,3768 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.59 \begin{figure} - [h] +l.5 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure}[ + H] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.7 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.7 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.9 \includegraphics + [scale=0.3]{Illustrations/Q4eigenValTEMPSCONT} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no V in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no E in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no S in font nullfont! +Missing character: There is no C in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no T in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 \caption + {Valeurs propres en temps continu.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.13 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.13 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.13 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.15 \includegraphics + [scale=0.3]{Illustrations/Q40100} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \caption + {$T_s = 0.01\,\mathrm{s}$.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.18 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.18 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.20 \includegraphics + [scale=0.3]{Illustrations/Q40200} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.21 \caption + {$T_s = 0.02\,\mathrm{s}$.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.22 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.24 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.24 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.26 \includegraphics + [scale=0.3]{Illustrations/Q40400} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no 0 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.27 \caption + {$T_s = 0.04\,\mathrm{s}$.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.28 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \caption + {Comparaison des valeurs propres du système en temps conti... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.31 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--32 +[] + [] + + +Overfull \hbox (20.67358pt too wide) in paragraph at lines 5--32 +\OML/cmm/m/it/10 T[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (23.3889pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 01 s$ + [] + + +Overfull \hbox (20.67358pt too wide) in paragraph at lines 5--32 +\OML/cmm/m/it/10 T[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (23.3889pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 02 s$ + [] + + +Overfull \hbox (20.67358pt too wide) in paragraph at lines 5--32 +\OML/cmm/m/it/10 T[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (23.3889pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 04 s$ + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 ^^Re + [] + +) (./Questions/Q5.tex + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.1 \textbf{Question 5} + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +Overfull \hbox (64.64003pt too wide) in paragraph at lines 1--2 +[]\OT1/cmr/bx/n/10 Question + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 1--2 +\OT1/cmr/bx/n/10 5 + [] + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.3 L + a Figure 2 montre que la sortie $y(t)$ oscille après l’échelon, con... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no 2 in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--4 +[] + [] + + +Overfull \hbox (16.65051pt too wide) in paragraph at lines 3--4 +\OML/cmm/m/it/10 y\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (7.22223pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 '^^Se + [] + + +Overfull \hbox (7.22223pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 '^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Re + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Missing \begin{document}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure}[ + H] +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.7 \includegraphics + [scale=0.4]{Illustrations/Q5stepReponse} % Remplacez... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.8 \caption + {Response du système en boucle ouverte.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +) (./Questions/Q6.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--2 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--2 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 5--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 5--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 5--2 +\OT1/cmr/bx/n/10 6 + [] + +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (41.7031pt too wide) in paragraph at lines 3--4 + \OML/cmm/m/it/10 x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (37.38528pt too wide) in paragraph at lines 3--4 + []\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 )$ + [] + + +Overfull \hbox (10.00002pt too wide) in paragraph at lines 3--4 + \OMS/cmsy/m/n/10 ) + [] + + +Overfull \hbox (38.92995pt too wide) in paragraph at lines 3--4 + \OML/cmm/m/it/10 w\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (65.9433pt too wide) in paragraph at lines 3--4 + [] [][] \OML/cmm/m/it/10 x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^V; t\/cmr/m/n/10 +)\OML/cmm/m/it/10 d^^V$ + [] + +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! + +Overfull \hbox (42.61572pt too wide) in paragraph at lines 5--5 + \OML/cmm/m/it/10 x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^V; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (53.07835pt too wide) in paragraph at lines 5--5 + \/cmr/m/n/10 ^^H[](\OML/cmm/m/it/10 ^^V\/cmr/m/n/10 )\OML/cmm/m/it/10 x[]\/cmr +/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no o in font nullfont! + +Overfull \hbox (5.55557pt too wide) in paragraph at lines 6--7 + []\/cmr/m/n/10 ^^Ru + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.10 \int\int_0^\zeta \Phi(\mu)d\mu & + 0_{{\rm I\!R}_{1\times4}} +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Undefined control sequence. +l.10 \int\int_0^\zeta \Phi(\mu)d\mu & 0_{{\rm + I\!R}_{1\times4}} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: \begin{equation} on input line 7 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \end{bmatrix} + x_d(t) +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (150.66171pt too wide) detected at line 12 +\OML/cmm/m/it/10 w\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = [] [][] + ^^H(\OML/cmm/m/it/10 ^^V\/cmr/m/n/10 )\OML/cmm/m/it/10 d^^V\/cmr/m/n/10 0[]\OM +L/cmm/m/it/10 x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + [] + +) +! Undefined control sequence. +l.19 \section + {Retour de sortie} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! +(./Questions/Q7.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 19--2 +[] + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 19--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 19--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (5.74997pt too wide) in paragraph at lines 19--2 +\OT1/cmr/bx/n/10 7 + [] + +Missing character: There is no N in font nullfont! 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+Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no : in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! 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LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure} + [H] Your command was ignored. Type I to replace it with another command, or to continue without it. Missing character: There is no [ in font nullfont! -Missing character: There is no h in font nullfont! +Missing character: There is no H in font nullfont! Missing character: There is no ] in font nullfont! ! Undefined control sequence. -l.61 \includegraphics - [width=0.5\textwidth]{example-image} % Remplacez pa... +l.7 \includegraphics + [scale=0.3]{Illustrations/Q8} % Remplacez par votre ... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.7 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.7 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.9 \includegraphics + [scale=0.3]{Illustrations/Q9continu} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 3 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 9 in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 \caption + {Valeurs propres en temps continu.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.13 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.13 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.13 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.15 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q9_TE001} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 9 in font nullfont! +! Missing $ inserted. + + $ +l.15 ...cale=0.4]{Illustrations/NouveauxImages/Q9_ + TE001} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.15 ....4]{Illustrations/NouveauxImages/Q9_TE001} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \caption + {$T_s = 0.01\,\mathrm{s}$.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.16 \caption{$ + T_s = 0.01\,\mathrm{s}$.} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.16 \caption{$T_ + s = 0.01\,\mathrm{s}$.} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.18 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.18 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.20 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q9_TE002} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 9 in font nullfont! +! Missing $ inserted. + + $ +l.20 ...cale=0.4]{Illustrations/NouveauxImages/Q9_ + TE002} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.20 ....4]{Illustrations/NouveauxImages/Q9_TE002} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.21 \caption + {$T_s = 0.02\,\mathrm{s}$.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.21 \caption{$ + T_s = 0.02\,\mathrm{s}$.} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.21 \caption{$T_ + s = 0.02\,\mathrm{s}$.} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.22 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.24 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.24 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.26 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q9_TE004} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 9 in font nullfont! +! Missing $ inserted. + + $ +l.26 ...cale=0.4]{Illustrations/NouveauxImages/Q9_ + TE004} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.26 ....4]{Illustrations/NouveauxImages/Q9_TE004} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.27 \caption + {$T_s = 0.04\,\mathrm{s}$.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +! Missing } inserted. + + } +l.27 \caption{$ + T_s = 0.04\,\mathrm{s}$.} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.27 \caption{$T_ + s = 0.04\,\mathrm{s}$.} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.28 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \caption + {Valeurs propres dans le cas d'un retour de sortie} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no V in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no e in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.31 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 4--32 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 4--32 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (20.69337pt too wide) in paragraph at lines 4--32 +\OML/cmm/m/it/10 T[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (86.28485pt too wide) in paragraph at lines 4--32 +\OMS/cmsy/m/n/10 f\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 01\OML/cmm/m/it/ +10 s\/cmr/m/n/10 ; 0\OML/cmm/m/it/10 :\/cmr/m/n/10 02\OML/cmm/m/it/10 s\/cmr/m/ +n/10 ; 0\OML/cmm/m/it/10 :\/cmr/m/n/10 04\OML/cmm/m/it/10 s\OMS/cmsy/m/n/10 g$ + [] + + +Overfull \hbox (44.08784pt too wide) in paragraph at lines 4--32 +[]\OML/cmm/m/it/10 E\/cmr/m/n/10 001[]$$[] = + [] + + +Overfull \hbox (23.3889pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 01 s$ + [] + + +Overfull \hbox (44.08784pt too wide) in paragraph at lines 4--32 +[]\OML/cmm/m/it/10 E\/cmr/m/n/10 002[]$$[] = + [] + + +Overfull \hbox (23.3889pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 02 s$ + [] + + +Overfull \hbox (44.08784pt too wide) in paragraph at lines 4--32 +[]\OML/cmm/m/it/10 E\/cmr/m/n/10 004[]$$[] = + [] + + +Overfull \hbox (23.3889pt too wide) in paragraph at lines 4--32 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 04 s$ + [] + +Missing character: There is no C in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no , in font nullfont! 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LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.6 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.8 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.8 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.8 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.10 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q10} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \caption + {Système sur le seuil: $T_s = 0.0356s$} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no : in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.12 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.14 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.14 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.14 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.16 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q10_di... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 0 in font nullfont! +! Missing $ inserted. + + $ +l.16 ...ale=0.4]{Illustrations/NouveauxImages/Q10_ + diverge} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.16 ...{Illustrations/NouveauxImages/Q10_diverge} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \caption + {Système hors le seuil: $T_s = 0.0366s$} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +LaTeX Warning: Command \` invalid in math mode on input line 17. + + +LaTeX Warning: Command \` invalid in math mode on input line 17. + +! Please use \mathaccent for accents in math mode. +\add@accent ... \let \ignorespaces \relax \accent + #1 #2\egroup \ifmmode \els... +l.17 \caption{Systè + me hors le seuil: $T_s = 0.0366s$} +I'm changing \accent to \mathaccent here; wish me luck. +(Accents are not the same in formulas as they are in text.) + +! Missing { inserted. + + \edef +l.17 \caption{Systè + me hors le seuil: $T_s = 0.0366s$} +A left brace was mandatory here, so I've put one in. +You might want to delete and/or insert some corrections +so that I will find a matching right brace soon. +(If you're confused by all this, try typing `I}' now.) + +! Missing } inserted. + + } +l.17 \caption{Système hors le seuil: $ + T_s = 0.0366s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.17 \caption{Système hors le seuil: $ + T_s = 0.0366s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.17 \caption{Système hors le seuil: $T_ + s = 0.0366s$} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.19 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 6--20 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 6--20 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (20.67358pt too wide) in paragraph at lines 6--20 +\OML/cmm/m/it/10 T[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (32.46536pt too wide) in paragraph at lines 6--20 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 0356\OML/cmm/m/it/10 s$ + [] + + +Overfull \hbox (140.90746pt too wide) in paragraph at lines 6--20 +[]\OML/cmm/m/it/10 iverge[]$$[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (32.46536pt too wide) in paragraph at lines 6--20 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 0366\OML/cmm/m/it/10 s$ + [] + +) +! Undefined control sequence. +l.29 \section + {Retour d'état} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +(./Questions/Q11.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 29--2 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 29--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 29--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 29--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 29--2 +\OT1/cmr/bx/n/10 11 + [] + +Missing character: There is no A in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--4 +[] + [] + + +Overfull \hbox (15.74986pt too wide) in paragraph at lines 3--4 +\OT1/cmtt/m/n/10 lqr + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--5 +[] + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.8 0.97 & + -14.62 & 0{,}66 & 1.32 & 19.32 & 0.39 & 2.40 & -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 0.97 & -14.62 & + 0{,}66 & 1.32 & 19.32 & 0.39 & 2.40 & -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 0.97 & -14.62 & 0{,}66 & + 1.32 & 19.32 & 0.39 & 2.40 & -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 0.97 & -14.62 & 0{,}66 & 1.32 & + 19.32 & 0.39 & 2.40 & -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 0.97 & -14.62 & 0{,}66 & 1.32 & 19.32 & + 0.39 & 2.40 & -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 0.97 & -14.62 & 0{,}66 & 1.32 & 19.32 & 0.39 & + 2.40 & -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.8 ....62 & 0{,}66 & 1.32 & 19.32 & 0.39 & 2.40 & + -2.11 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 5 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (190.31984pt too wide) detected at line 10 +\OML/cmm/m/it/10 K \/cmr/m/n/10 = 0\OML/cmm/m/it/10 :\/cmr/m/n/10 97 \OMS/cmsy/ +m/n/10 ^^@ \/cmr/m/n/10 14\OML/cmm/m/it/10 :\/cmr/m/n/10 620[]661\OML/cmm/m/it/ +10 :\/cmr/m/n/10 3219\OML/cmm/m/it/10 :\/cmr/m/n/10 320\OML/cmm/m/it/10 :\/cmr/ +m/n/10 392\OML/cmm/m/it/10 :\/cmr/m/n/10 40 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 2 +\OML/cmm/m/it/10 :\/cmr/m/n/10 11 + [] + +) (./Questions/Q12.tex +Overfull \hbox (28.6679pt too wide) in paragraph at lines 10--2 + \OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 10--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 10--2 +\OT1/cmr/bx/n/10 12 + [] + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ...: Reference `fig:Q15' on page \thepage + \space undefined\on@line . +l.3 La Figure~\ref{fig:Q15} + montre que le système en boucle fermée suit co... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `fig:Q15' on page undefined on input line 3. + +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no . in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--4 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 3--4 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (8.88889pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se + [] + + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.7 \includegraphics + [width=0.4\textwidth]{Illustrations/Q12} % Remplacez... The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct @@ -1050,12 +6511,12 @@ Missing character: There is no h in font nullfont! Missing character: There is no = in font nullfont! Missing character: There is no 0 in font nullfont! Missing character: There is no . in font nullfont! -Missing character: There is no 5 in font nullfont! +Missing character: There is no 4 in font nullfont! ! Missing number, treated as zero. ] -l.61 \includegraphics[width=0.5\textwidth] - {example-image} % Remplacez pa... +l.7 \includegraphics[width=0.4\textwidth] + {Illustrations/Q12} % Remplacez... A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, look up `weird error' in the index to The TeXbook.) @@ -1063,8 +6524,8 @@ look up `weird error' in the index to The TeXbook.) ! Illegal unit of measure (pt inserted). ] -l.61 \includegraphics[width=0.5\textwidth] - {example-image} % Remplacez pa... +l.7 \includegraphics[width=0.4\textwidth] + {Illustrations/Q12} % Remplacez... Dimensions can be in units of em, ex, in, pt, pc, cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! I'll assume that you meant to say pt, for printer's points. @@ -1073,19 +6534,23 @@ delete the erroneous units; e.g., type `2' to delete two letters. (See Chapter 27 of The TeXbook.) Missing character: There is no ] in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no x in font nullfont! -Missing character: There is no a in font nullfont! -Missing character: There is no m in font nullfont! -Missing character: There is no p in font nullfont! +Missing character: There is no I in font nullfont! Missing character: There is no l in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no - in font nullfont! -Missing character: There is no i in font nullfont! -Missing character: There is no m in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! -Missing character: There is no g in font nullfont! -Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 2 in font nullfont! ! LaTeX Error: \caption outside float. @@ -1093,34 +6558,56 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.62 \caption - {Ceci est un exemple de figure.} +l.8 \caption + {Simulation numérique du système continu en boucle fermée.} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. -Missing character: There is no C in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no c in font nullfont! +Missing character: There is no S in font nullfont! Missing character: There is no i in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no x in font nullfont! -Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! -Missing character: There is no p in font nullfont! +Missing character: There is no u in font nullfont! Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no f in font nullfont! -Missing character: There is no i in font nullfont! -Missing character: There is no g in font nullfont! -Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no . in font nullfont! @@ -1130,33 +6617,267 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.64 \end{figure} +l.10 \end{figure} Your command was ignored. Type I to replace it with another command, or to continue without it. - -Overfull \hbox (20.0pt too wide) in paragraph at lines 58--65 +) +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--32 [] [] -! LaTeX Error: Environment table undefined. +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--32 +\/cmr/m/n/10 ^^Se + [] + +! Undefined control sequence. +l.33 \subsection + {Retour d'état par ZOH} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no Z in font nullfont! +Missing character: There is no O in font nullfont! +Missing character: There is no H in font nullfont! +(./Questions/Q13.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 33--2 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 33--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 33--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 33--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 33--2 +\OT1/cmr/bx/n/10 13 + [] + +Missing character: There is no A in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no h in font nullfont! 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LaTeX Error: Environment figure undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.66 \begin{table} - [h] +l.5 \begin{figure} + [H] Your command was ignored. Type I to replace it with another command, or to continue without it. Missing character: There is no [ in font nullfont! -Missing character: There is no h in font nullfont! +Missing character: There is no H in font nullfont! Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.7 \includegraphics + [scale=0.5]{Illustrations/NouveauxImages/Q13} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). 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LaTeX Error: \caption outside float. @@ -1164,341 +6885,3509 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.68 \caption - {Ceci est un exemple de tableau.} +l.8 \caption + {Pôles du système avec temps d'echantillonnage: $T_e = 0.0... + You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. -Missing character: There is no C in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no c in font nullfont! -Missing character: There is no i in font nullfont! +Missing character: There is no P in font nullfont! +Missing character: There is no l in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! -Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! 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LaTeX Error: \begin{document} ended by \end{table}. +! LaTeX Error: \begin{document} ended by \end{figure}. See the LaTeX manual or LaTeX Companion for explanation. 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LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.7 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.7 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.9 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q14} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 4 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 \caption + {Système sur le seuil: $T_s = 0.0107s$} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no : in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.13 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.13 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.13 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.15 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q14_in... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 4 in font nullfont! +! Missing $ inserted. + + $ +l.15 ...ale=0.4]{Illustrations/NouveauxImages/Q14_ + instable} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.15 ...Illustrations/NouveauxImages/Q14_instable} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \caption + {Système hors le seuil: $T_s = 0.0108s$} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +LaTeX Warning: Command \` invalid in math mode on input line 16. + + +LaTeX Warning: Command \` invalid in math mode on input line 16. + +! Please use \mathaccent for accents in math mode. +\add@accent ... \let \ignorespaces \relax \accent + #1 #2\egroup \ifmmode \els... +l.16 \caption{Systè + me hors le seuil: $T_s = 0.0108s$} +I'm changing \accent to \mathaccent here; wish me luck. +(Accents are not the same in formulas as they are in text.) + +! Missing { inserted. + + \edef +l.16 \caption{Systè + me hors le seuil: $T_s = 0.0108s$} +A left brace was mandatory here, so I've put one in. +You might want to delete and/or insert some corrections +so that I will find a matching right brace soon. +(If you're confused by all this, try typing `I}' now.) + +! Missing } inserted. + + } +l.16 \caption{Système hors le seuil: $ + T_s = 0.0108s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.16 \caption{Système hors le seuil: $ + T_s = 0.0108s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.16 \caption{Système hors le seuil: $T_ + s = 0.0108s$} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.18 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.18 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.20 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q14_step} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 4 in font nullfont! +! Missing $ inserted. + + $ +l.20 ...ale=0.4]{Illustrations/NouveauxImages/Q14_ + step} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.20 ....4]{Illustrations/NouveauxImages/Q14_step} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.21 \caption + {Reponse à un echelon unitaire: $T_s = 0.0107s$} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +LaTeX Warning: Command \` invalid in math mode on input line 21. + + +LaTeX Warning: Command \` invalid in math mode on input line 21. + +! Please use \mathaccent for accents in math mode. +\add@accent ... \let \ignorespaces \relax \accent + #1 #2\egroup \ifmmode \els... +l.21 \caption{Reponse à + un echelon unitaire: $T_s = 0.0107s$} +I'm changing \accent to \mathaccent here; wish me luck. +(Accents are not the same in formulas as they are in text.) + +! Missing { inserted. + + \edef +l.21 \caption{Reponse à + un echelon unitaire: $T_s = 0.0107s$} +A left brace was mandatory here, so I've put one in. +You might want to delete and/or insert some corrections +so that I will find a matching right brace soon. +(If you're confused by all this, try typing `I}' now.) + +! Missing } inserted. + + } +l.21 ...\caption{Reponse à un echelon unitaire: $ + T_s = 0.0107s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.21 ...\caption{Reponse à un echelon unitaire: $ + T_s = 0.0107s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.21 ...aption{Reponse à un echelon unitaire: $T_ + s = 0.0107s$} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.22 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.24 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.24 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.24 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.26 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q14_st... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 4 in font nullfont! +! Missing $ inserted. + + $ +l.26 ...ale=0.4]{Illustrations/NouveauxImages/Q14_ + step_diverge} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Extra }, or forgotten $. +l.26 ...strations/NouveauxImages/Q14_step_diverge} + +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.27 \caption + {Reponse à un echelon unitaire: $T_s = 0.0108s$} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + + +LaTeX Warning: Command \` invalid in math mode on input line 27. + + +LaTeX Warning: Command \` invalid in math mode on input line 27. + +! Please use \mathaccent for accents in math mode. +\add@accent ... \let \ignorespaces \relax \accent + #1 #2\egroup \ifmmode \els... +l.27 \caption{Reponse à + un echelon unitaire: $T_s = 0.0108s$} +I'm changing \accent to \mathaccent here; wish me luck. +(Accents are not the same in formulas as they are in text.) + +! Missing { inserted. + + \edef +l.27 \caption{Reponse à + un echelon unitaire: $T_s = 0.0108s$} +A left brace was mandatory here, so I've put one in. +You might want to delete and/or insert some corrections +so that I will find a matching right brace soon. +(If you're confused by all this, try typing `I}' now.) + +! Missing } inserted. + + } +l.27 ...caption{Reponse à un echelon unitaire: $ + T_s = 0.0108s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing } inserted. + + } +l.27 ...caption{Reponse à un echelon unitaire: $ + T_s = 0.0108s$} +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no T in font nullfont! +! Missing $ inserted. + + $ +l.27 ...ption{Reponse à un echelon unitaire: $T_ + s = 0.0108s$} +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.28 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.29 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +) +Overfull \hbox (20.0pt too wide) in paragraph at lines 5--36 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--36 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (20.67358pt too wide) in paragraph at lines 5--36 +\OML/cmm/m/it/10 T[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (32.46536pt too wide) in paragraph at lines 5--36 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 0107\OML/cmm/m/it/10 s$ + [] + + +Overfull \hbox (143.40771pt too wide) in paragraph at lines 5--36 +[]\OML/cmm/m/it/10 nstable[]$$[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (32.46536pt too wide) in paragraph at lines 5--36 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 0108\OML/cmm/m/it/10 s$ + [] + + +Overfull \hbox (162.91376pt too wide) in paragraph at lines 5--36 +[]\OML/cmm/m/it/10 tep[]$$[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (32.46536pt too wide) in paragraph at lines 5--36 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 0107\OML/cmm/m/it/10 s$ + [] + + +Overfull \hbox (195.45813pt too wide) in paragraph at lines 5--36 +[]\OML/cmm/m/it/10 tep[]iverge[]$$[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (32.46536pt too wide) in paragraph at lines 5--36 +\/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/m/n/10 0108\OML/cmm/m/it/10 s$ + [] + +! Undefined control sequence. +l.38 \section + {Rejet de perturbation} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no j in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +(./Questions/Q15.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 38--2 +[] + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 38--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 38--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 38--2 +\OT1/cmr/bx/n/10 15 + [] + +Missing character: There is no S in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! + +Overfull \hbox (36.3246pt too wide) in paragraph at lines 3--4 + \OML/cmm/m/it/10 q\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (20.33917pt too wide) in paragraph at lines 3--4 + \OML/cmm/m/it/10 q[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + + +Overfull \hbox (28.83575pt too wide) in paragraph at lines 3--4 + \OML/cmm/m/it/10 F[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (79.96356pt too wide) in paragraph at lines 3--4 + \OMS/cmsy/m/n/10 ^^@ [][] \/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\ +OML/cmm/m/it/10 q\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P; t\/cmr/m/n/10 )\OML/cmm/m/ +it/10 d^^P$ + [] + + +Overfull \hbox (10.00002pt too wide) in paragraph at lines 3--4 + \OMS/cmsy/m/n/10 , + [] + + +Overfull \hbox (28.83575pt too wide) in paragraph at lines 3--4 + \OML/cmm/m/it/10 F[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (62.71419pt too wide) in paragraph at lines 3--4 + \OMS/cmsy/m/n/10 ^^@ [][] \/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OM +L/cmm/m/it/10 q[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + +Missing character: There is no O in font nullfont! +Missing character: There is no r in font nullfont! + +Overfull \hbox (32.8781pt too wide) in paragraph at lines 5--7 + \OML/cmm/m/it/10 E[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (56.16539pt too wide) in paragraph at lines 5--7 + \OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 D[]x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/c +mr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (46.6969pt too wide) in paragraph at lines 5--7 + \/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/m/it/10 u\/cmr/m/n/1 +0 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (18.28024pt too wide) in paragraph at lines 5--7 + \OML/cmm/m/it/10 F[]$ + [] + + +Overfull \hbox (10.00002pt too wide) in paragraph at lines 5--7 + \OMS/cmsy/m/n/10 ,$ + [] + + +Overfull \hbox (24.91978pt too wide) in paragraph at lines 5--7 + [] \/cmr/m/n/10 = + [] + + +Overfull \hbox (74.85985pt too wide) in paragraph at lines 5--7 + \OMS/cmsy/m/n/10 ^^@\OML/cmm/m/it/10 E[]D[]x[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t +\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ + [] + + +Overfull \hbox (65.39136pt too wide) in paragraph at lines 5--7 + \OML/cmm/m/it/10 E[]\/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm/ +m/it/10 u\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + + [] + + +Overfull \hbox (85.4503pt too wide) in paragraph at lines 5--7 + \OML/cmm/m/it/10 E[] [][] \/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\ +OML/cmm/m/it/10 d^^Pq[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + +Missing character: There is no D in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no o in font nullfont! + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.8 ...\dot{x}_d(t)=Ax_d(t)+Bu(t)+ \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Undefined control sequence. +l.9 0_{\rm + I\!R_{_{4\times1}}} \\ E^{-1}\int_0^L\Phi(\zeta)d\zeta +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +! LaTeX Error: There's no line here to end. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 0_{\rm I\!R_{_{4\times1}}} \\ + E^{-1}\int_0^L\Phi(\zeta)d\zeta +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.9 0_{\rm I\!R_{_{4\times1}}} \\ + E^{-1}\int_0^L\Phi(\zeta)d\zeta +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + +! Missing } inserted. + + } +l.9 0_{\rm I\!R_{_{4\times1}}} \\ + E^{-1}\int_0^L\Phi(\zeta)d\zeta +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +! Missing \endgroup inserted. + + \endgroup +l.9 0_{\rm I\!R_{_{4\times1}}} \\ + E^{-1}\int_0^L\Phi(\zeta)d\zeta +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + + +Overfull \hbox (5.55557pt too wide) in paragraph at lines 8--9 + []\/cmr/m/n/10 ^^Ru + [] + + +Overfull \hbox (32.32257pt too wide) in paragraph at lines 8--9 + []\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = + [] + + +Overfull \hbox (37.04488pt too wide) in paragraph at lines 8--9 + \OML/cmm/m/it/10 Ax[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + + [] + + +Overfull \hbox (32.9781pt too wide) in paragraph at lines 8--9 + \OML/cmm/m/it/10 Bu\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) + + [] + + +Overfull \hbox (27.46915pt too wide) in paragraph at lines 8--9 + \/cmr/m/n/10 0[][]$ + [] + +! Extra }, or forgotten \endgroup. +\par ...m \@noitemerr {\@@par }\fi \else {\@@par } + \fi +l.9 0_{\rm I\!R_{_{4\times1}}} \\ + E^{-1}\int_0^L\Phi(\zeta)d\zeta +I've deleted a group-closing symbol because it seems to be +spurious, as in `$x}$'. But perhaps the } is legitimate and +you forgot something else, as in `\hbox{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. + +Missing character: There is no E in font nullfont! +! Missing $ inserted. + + $ +l.9 0_{\rm I\!R_{_{4\times1}}} \\ E^ + {-1}\int_0^L\Phi(\zeta)d\zeta +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +! LaTeX Error: \begin{center} on input line 2 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 \end{bmatrix} + q_0(t)$ +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Missing $ inserted. + + $ +l.10 \end{bmatrix} + q_0(t)$ +I've inserted something that you may have forgotten. +(See the above.) +With luck, this will get me unwedged. But if you +really didn't forget anything, try typing `2' now; then +my insertion and my current dilemma will both disappear. + +Missing character: There is no q in font nullfont! +! Missing $ inserted. + + $ +l.10 \end{bmatrix}q_ + 0(t)$ +I've inserted a begin-math/end-math symbol since I think +you left one out. Proceed, with fingers crossed. + + +Overfull \hbox (73.02786pt too wide) in paragraph at lines 9--11 +[]$[] [][] \/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/10 +d^^P$$[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$ + [] + + +! LaTeX Error: \begin{document} ended by \end{center}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \end{center} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Extra \endgroup. + \endgroup + +l.11 \end{center} + +Things are pretty mixed up, but I think the worst is over. + +Missing character: There is no A in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 12--13 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 12--13 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (12.20743pt too wide) in paragraph at lines 12--13 +\OML/cmm/m/it/10 B[]$ + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.15 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{equation} on input line 13 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.19 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.20 0 & + 0 & 0 & 0 & 1 & 1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.20 0 & 0 & + 0 & 0 & 1 & 1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.20 0 & 0 & 0 & + 0 & 1 & 1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.20 0 & 0 & 0 & 0 & + 1 & 1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.20 0 & 0 & 0 & 0 & 1 & + 1 & 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.20 0 & 0 & 0 & 0 & 1 & 1 & + 0 & 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.20 0 & 0 & 0 & 0 & 1 & 1 & 0 & + 0 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 13 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.21 \end{bmatrix} + ^{T} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (166.39594pt too wide) detected at line 22 +\OML/cmm/m/it/10 B[] \/cmr/m/n/10 = 0[] \OMS/cmsy/m/n/10 ^^@ \OML/cmm/m/it/10 +E[] [][] \/cmr/m/n/10 ^^H(\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/10 d^ +^P \/cmr/m/n/10 = 00001100[] + [] + +) (./Questions/Q16.tex +Overfull \hbox (64.64003pt too wide) in paragraph at lines 1--2 +[]\OT1/cmr/bx/n/10 Question + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 1--2 +\OT1/cmr/bx/n/10 16 + [] + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ...fig:q16_perturbation' on page \thepage + \space undefined\on@line . +l.3 La Figure~\ref{fig:q16_perturbation} + montre que le système ne corrige p... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `fig:q16_perturbation' on page undefined on input lin +e 3. + +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.4 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! +! Undefined control sequence. +l.6 \includegraphics + [scale=0.4]{Illustrations/NouveauxImages/Q16} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 6 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \caption + {Simulation du système avec une perturbation.} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 \end{figure} Your command was ignored. Type I to replace it with another command, or to continue without it. -Overfull \hbox (20.0pt too wide) in paragraph at lines 66--77 +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--10 [] [] -Overfull \hbox (13.33337pt too wide) in paragraph at lines 66--77 +Overfull \hbox (10.86105pt too wide) in paragraph at lines 3--10 [] [] -! Undefined control sequence. -l.78 \section - {Another section} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. -Missing character: There is no A in font nullfont! -Missing character: There is no n in font nullfont! +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--10 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--10 +\/cmr/m/n/10 ^^Ra + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--10 +\/cmr/m/n/10 ^^Re + [] + +Missing character: There is no P in font nullfont! Missing character: There is no o in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no h in font nullfont! -Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no s in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no c in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no i in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no n in font nullfont! -! Undefined control sequence. -l.79 \subsection - {Une sous section} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - -Missing character: There is no U in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no s in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no s in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no r in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no i in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no n in font nullfont! -! Undefined control sequence. -l.80 \subsubsection - {Une sous sous section} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - -Missing character: There is no U in font nullfont! -Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! -Missing character: There is no s in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no e in font nullfont! -Missing character: There is no c in font nullfont! -Missing character: There is no t in font nullfont! -Missing character: There is no i in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no U in font nullfont! -Missing character: There is no n in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no l in font nullfont! 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Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! +) +Overfull \hbox (20.0pt too wide) in paragraph at lines 11--41 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 11--41 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 11--41 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 11--41 +\/cmr/m/n/10 ^^Se + [] + +! Undefined control sequence. +l.42 \subsection + {Remplacement du pré-gain H} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no R in font nullfont! +Missing character: There is no e in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no l in font nullfont! -Missing character: There is no i in font nullfont! -Missing character: There is no q in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no d in font nullfont! Missing character: There is no u in font nullfont! -! Undefined control sequence. -\@footnotetext ...tins {\reset@font \footnotesize - \interlinepenalty \interfo... -l.81 ...mpliqué\footnote{Une note de bas de page} - -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - -! Undefined control sequence. -\@footnotetext ...}\color@begingroup \@makefntext - {\rule \z@ \footnotesep \i... -l.81 ...mpliqué\footnote{Une note de bas de page} - -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. - - -Overfull \hbox (17.50003pt too wide) in paragraph at lines 81--81 -[][]\/cmr/m/n/10 Une - [] - - -Overfull \hbox (18.88893pt too wide) in paragraph at lines 81--81 -\/cmr/m/n/10 note - [] - - -Overfull \hbox (10.00002pt too wide) in paragraph at lines 81--81 -\/cmr/m/n/10 de - [] - - -Overfull \hbox (14.50003pt too wide) in paragraph at lines 81--81 -\/cmr/m/n/10 bas - [] - - -Overfull \hbox (10.00002pt too wide) in paragraph at lines 81--81 -\/cmr/m/n/10 de - [] - - -Overfull \hbox (20.00005pt too wide) in paragraph at lines 81--81 -\/cmr/m/n/10 page| - [] - - -Overfull \hbox (20.0pt too wide) in paragraph at lines 78--82 +Missing character: There is no p in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no - in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no H in font nullfont! +(./Questions/Q17.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 42--2 [] [] -Overfull \hbox (8.93057pt too wide) in paragraph at lines 78--82 -\/cmr/m/n/10 ^^Se[] +Overfull \hbox (4.44444pt too wide) in paragraph at lines 42--2 +\/cmr/m/n/10 ^^Se [] -! LaTeX Error: The font size command \normalsize is not defined: - there is probably something wrong with the class file. +Overfull \hbox (28.6679pt too wide) in paragraph at lines 42--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 42--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 42--2 +\OT1/cmr/bx/n/10 17 + [] + +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no h in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no i in font nullfont! 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+Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (27.50002pt too wide) in paragraph at lines 3--5 +[][]\/cmr/m/n/10 A + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^o + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^o + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Ra + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (18.91605pt too wide) in paragraph at lines 3--5 +\OML/cmm/m/it/10 p[] \/cmr/m/n/10 = + [] + + +Overfull \hbox (35.55566pt too wide) in paragraph at lines 3--5 +\OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 4\OML/cmm/m/it/10 :\/cmr/m/n/10 3805$ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^o + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^o + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--5 +\/cmr/m/n/10 ^^Se + [] + +! Undefined control sequence. +l.6 $p_{\text + {des}} =$ +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +Overfull \hbox (27.81807pt too wide) in paragraph at lines 6--7 + \OML/cmm/m/it/10 p[] \/cmr/m/n/10 =$ + [] + + +! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.83 \newpage - +l.8 \begin{bmatrix} + Your command was ignored. Type I to replace it with another command, or to continue without it. -[2{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} -! Undefined control sequence. - \newlabel{fig:example}{{}{\thepage - }{}{}{}} -l.83 \newpage +! Misplaced alignment tab character &. +l.9 -85 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.10 -8+69i & -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. -\newlabel{fig:example}{{}{}{}{}{}} -! Undefined control sequence. - \newlabel{tab:example}{{}{\thepage - }{}{}{}} -l.83 \newpage +! Misplaced alignment tab character &. +l.11 -8-69i & -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. -\newlabel{tab:example}{{}{}{}{}{}} -] -! Undefined control sequence. -l.84 \psection - {Conclusion} -The control sequence at the end of the top line -of your error message was never \def'ed. If you have -misspelled it (e.g., `\hobx'), type `I' and the correct -spelling (e.g., `I\hbox'). Otherwise just continue, -and I'll forget about whatever was undefined. +! Misplaced alignment tab character &. +l.12 -28+17i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. -Missing character: There is no C in font nullfont! +! Misplaced alignment tab character &. +l.13 -28-17i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.14 -16 & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.15 -4+3i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.16 -4-3i & + +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 7 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.18 \end{bmatrix} + ^{T} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (258.6378pt too wide) detected at line 19 +\OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 85 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 8 + 69\OM +L/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 8 \OMS/cmsy/m/n/10 ^^@ \/cmr/ +m/n/10 69\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 28 + 17\OML/cmm/m +/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 28 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 + 17\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 16 \OMS/cmsy/m/n/10 ^^@ + \/cmr/m/n/10 4 + 3\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 4 \OMS/ +cmsy/m/n/10 ^^@ \/cmr/m/n/10 3\OML/cmm/m/it/10 i \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n +/10 4[] + [] + +) (./Questions/Q18.tex +Overfull \hbox (44.64003pt too wide) in paragraph at lines 1--2 +\OT1/cmr/bx/n/10 Question + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 1--2 +\OT1/cmr/bx/n/10 18 + [] + +Missing character: There is no E in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no f in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no c in font nullfont! -Missing character: There is no l in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! -Missing character: There is no U in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no M in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no T in font nullfont! +Missing character: There is no L in font nullfont! +Missing character: There is no A in font nullfont! +Missing character: There is no B in font nullfont! +Missing character: There is no , in font nullfont! Missing character: There is no n in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no : in font nullfont! + +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--4 +[] + [] + + +Overfull \hbox (26.24977pt too wide) in paragraph at lines 3--4 +\OT1/cmtt/m/n/10 place + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (12.97919pt too wide) in paragraph at lines 3--4 +\OML/cmm/m/it/10 K[]$ + [] + + +Overfull \hbox (11.82234pt too wide) in paragraph at lines 3--4 +\OML/cmm/m/it/10 K[]$ + [] + + +Overfull \hbox (5.00002pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Ra + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--4 +\/cmr/m/n/10 ^^Se + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.5 K_{Aug} = \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.6 K_1 & + K_i +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 4 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.7 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (62.02223pt too wide) detected at line 8 +\OML/cmm/m/it/10 K[] \/cmr/m/n/10 = \OML/cmm/m/it/10 K[]K[] + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.11 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +! Misplaced alignment tab character &. +l.12 -3.1081 & + -18.9367 & -0.1707 & 2.1192 & 19.4677 & -2.3049 & 2.3377 & -1... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 -3.1081 & -18.9367 & + -0.1707 & 2.1192 & 19.4677 & -2.3049 & 2.3377 & -1... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 -3.1081 & -18.9367 & -0.1707 & + 2.1192 & 19.4677 & -2.3049 & 2.3377 & -1... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 -3.1081 & -18.9367 & -0.1707 & 2.1192 & + 19.4677 & -2.3049 & 2.3377 & -1... +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 ... & -18.9367 & -0.1707 & 2.1192 & 19.4677 & + -2.3049 & 2.3377 & -1.7524 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 ...7 & -0.1707 & 2.1192 & 19.4677 & -2.3049 & + 2.3377 & -1.7524 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + +! Misplaced alignment tab character &. +l.12 ...07 & 2.1192 & 19.4677 & -2.3049 & 2.3377 & + -1.7524 +I can't figure out why you would want to use a tab mark +here. If you just want an ampersand, the remedy is +simple: Just type `I\&' now. But if some right brace +up above has ended a previous alignment prematurely, +you're probably due for more error messages, and you +might try typing `S' now just to see what is salvageable. + + +! LaTeX Error: \begin{equation} on input line 9 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.13 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (297.42435pt too wide) detected at line 14 +\OML/cmm/m/it/10 K[] \/cmr/m/n/10 = \OMS/cmsy/m/n/10 ^^@\/cmr/m/n/10 3\OML/cmm/ +m/it/10 :\/cmr/m/n/10 1081 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 18\OML/cmm/m/it/10 + :\/cmr/m/n/10 9367 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 0\OML/cmm/m/it/10 :\/cmr/ +m/n/10 17072\OML/cmm/m/it/10 :\/cmr/m/n/10 119219\OML/cmm/m/it/10 :\/cmr/m/n/10 + 4677 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 2\OML/cmm/m/it/10 :\/cmr/m/n/10 30492\O +ML/cmm/m/it/10 :\/cmr/m/n/10 3377 \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 1\OML/cmm/m +/it/10 :\/cmr/m/n/10 7524 + [] + + +! LaTeX Error: Environment bmatrix undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \begin{equation} on input line 15 ended by \end{bmatrix}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.19 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +Overfull \hbox (57.93344pt too wide) detected at line 20 +\OML/cmm/m/it/10 K[] \/cmr/m/n/10 = 26\OML/cmm/m/it/10 :\/cmr/m/n/10 2831 + [] + +) (./Questions/Q19.tex +Overfull \hbox (28.6679pt too wide) in paragraph at lines 20--2 + \OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 20--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 20--2 +\OT1/cmr/bx/n/10 19 + [] + +Missing character: There is no L in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no F in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +! Undefined control sequence. + ...e `fig:q19_integrale' on page \thepage + \space undefined\on@line . +l.3 La Figure~\ref{fig:q19_integrale} + montre qu'avec l'action intégrale, la... +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + + +LaTeX Warning: Reference `fig:q19_integrale' on page undefined on input line 3 +. + +Missing character: There is no m in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no q in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no c in font nullfont! -Missing character: There is no o in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no c in font nullfont! Missing character: There is no l in font nullfont! -Missing character: There is no u in font nullfont! -Missing character: There is no s in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! -) +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no , in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no b in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no j in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no ' in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: Environment figure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.4 \begin{figure} + [H] +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no [ in font nullfont! +Missing character: There is no H in font nullfont! +Missing character: There is no ] in font nullfont! + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.6 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.6 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.6 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.8 \includegraphics + [scale=0.5]{Illustrations/NouveauxImages/Q19} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 9 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.9 \caption + {Erreur en regime permanente} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no E in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.10 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: Environment subfigure undefined. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.12 \begin{subfigure} + {0.48\textwidth} +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 4 in font nullfont! +Missing character: There is no 8 in font nullfont! +! Missing number, treated as zero. + + } +l.12 \begin{subfigure}{0.48\textwidth} + +A number should have been here; I inserted `0'. +(If you can't figure out why I needed to see a number, +look up `weird error' in the index to The TeXbook.) + +! Illegal unit of measure (pt inserted). + + } +l.12 \begin{subfigure}{0.48\textwidth} + +Dimensions can be in units of em, ex, in, pt, pc, +cm, mm, dd, cc, nd, nc, bp, or sp; but yours is a new one! +I'll assume that you meant to say pt, for printer's points. +To recover gracefully from this error, it's best to +delete the erroneous units; e.g., type `2' to delete +two letters. (See Chapter 27 of The TeXbook.) + +! Undefined control sequence. +l.14 \includegraphics + [scale=0.5]{Illustrations/NouveauxImages/Q18} +The control sequence at the end of the top line +of your error message was never \def'ed. If you have +misspelled it (e.g., `\hobx'), type `I' and the correct +spelling (e.g., `I\hbox'). Otherwise just continue, +and I'll forget about whatever was undefined. + +Missing character: There is no [ in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no = in font nullfont! +Missing character: There is no 0 in font nullfont! +Missing character: There is no . in font nullfont! +Missing character: There is no 5 in font nullfont! +Missing character: There is no ] in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no N in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no x in font nullfont! +Missing character: There is no I in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no / in font nullfont! +Missing character: There is no Q in font nullfont! +Missing character: There is no 1 in font nullfont! +Missing character: There is no 8 in font nullfont! + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.15 \caption + {Erreur nulle en regime permanente} +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no E in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no e in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{subfigure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.16 \end{subfigure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + + +! LaTeX Error: \caption outside float. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.17 \caption + {Simulation du système avec correction par action intégra... + +You're in trouble here. Try typing to proceed. +If that doesn't work, type X to quit. + +Missing character: There is no S in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no d in font nullfont! +Missing character: There is no u in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no y in font nullfont! +Missing character: There is no s in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no m in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no v in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no p in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no c in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no o in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no i in font nullfont! +Missing character: There is no n in font nullfont! +Missing character: There is no t in font nullfont! +Missing character: There is no g in font nullfont! +Missing character: There is no r in font nullfont! +Missing character: There is no a in font nullfont! +Missing character: There is no l in font nullfont! +Missing character: There is no e in font nullfont! +Missing character: There is no . in font nullfont! + +! LaTeX Error: \begin{document} ended by \end{figure}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.19 \end{figure} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. + +) (./Questions/Q20.tex +Overfull \hbox (20.0pt too wide) in paragraph at lines 3--2 +[] + [] + + +Overfull \hbox (10.86105pt too wide) in paragraph at lines 3--2 +[] + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--2 +\/cmr/m/n/10 ^^Re + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 3--2 +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (28.6679pt too wide) in paragraph at lines 3--2 +\OT1/cmr/bx/n/10 Ques- + [] + + +Overfull \hbox (19.80545pt too wide) in paragraph at lines 3--2 +\OT1/cmr/bx/n/10 tion + [] + + +Overfull \hbox (11.49994pt too wide) in paragraph at lines 3--2 +\OT1/cmr/bx/n/10 20 + [] + +Missing character: There is no N in font nullfont! 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