diff --git a/BE_Brouillon.pdf b/BE_Brouillon.pdf new file mode 100644 index 0000000..088af3e Binary files /dev/null and b/BE_Brouillon.pdf differ diff --git a/BE_Sujet.pdf b/BE_Sujet.pdf new file mode 100644 index 0000000..d881c63 Binary files /dev/null and b/BE_Sujet.pdf differ diff --git a/latex/contents.log b/latex/contents.log index 5219856..bc88fc5 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) 16 APR 2026 22:36 +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 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -76,7 +76,7 @@ or to continue without it. [1] ! Undefined control sequence. l.5 \section - {Be Commande Numérique} + {Dynamique du système avec équations differentielles partielles} 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 @@ -90,24 +90,26 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.5 \section{B - e Commande Numérique} +l.5 \section{D + ynamique du système avec équations differentielles partielles} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. -Missing character: There is no B 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 D in font nullfont! +Missing character: There is no y 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 N 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 m 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! LaTeX Font Info: Trying to load font information for +cmr on input line 5. LaTeX Font Info: No file cmr.fd. on input line 5. @@ -117,8 +119,8 @@ LaTeX Font Warning: Font shape `/cmr/m/n' undefined ! Corrupted NFSS tables. wrong@fontshape ...message {Corrupted NFSS tables} error@fontshape else let f... -l.5 \section{Be Commande Numé - rique} +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, @@ -128,51 +130,97 @@ 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 r 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 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 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 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! +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 e 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 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 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 - {Identification du système} + {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 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 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 f 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 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 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 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 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 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 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 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 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 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 s in font nullfont! Missing character: There is no : in font nullfont! Overfull \hbox (20.0pt too wide) in paragraph at lines 5--8 @@ -181,12 +229,22 @@ Overfull \hbox (20.0pt too wide) in paragraph at lines 5--8 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 \/cmr/m/n/10 ^^Se [] Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--8 -\/cmr/m/n/10 ^^Re +\/cmr/m/n/10 ^^Se + [] + + +Overfull \hbox (4.44444pt too wide) in paragraph at lines 5--8 +\/cmr/m/n/10 ^^Se [] @@ -196,467 +254,746 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.9 B - E Commande Numérique +l.9 \begin{center} + You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. -Missing character: There is no B 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 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! -Overfull \hbox (20.0pt too wide) in paragraph at lines 9--10 -[] +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. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <5> on input line 10. -Overfull \hbox (4.44444pt too wide) in paragraph at lines 9--10 -\/cmr/m/n/10 ^^Se - [] - - -! LaTeX Error: Missing \begin{document}. +! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.11 Q - uestion 1) -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - -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 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 1 in font nullfont! -Missing character: There is no ) in font nullfont! - -Overfull \hbox (20.0pt too wide) in paragraph at lines 11--12 -[] - [] +l.11 ...rtial^2}{\partial \zeta ^2}\begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. -! LaTeX Error: Missing \begin{document}. +! LaTeX Error: \begin{equation} on input line 10 ended by \end{bmatrix}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.13 C - onsidering the following PDE model : -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. +l.13 \end{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. -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 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 i in font nullfont! -Missing character: There is no n in font nullfont! -Missing character: There is no g 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 f in font nullfont! -Missing character: There is no o 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 o in font nullfont! -Missing character: There is no w 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 g in font nullfont! -Missing character: There is no P 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 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 l 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 (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: Missing \begin{document}. +Overfull \hbox (18.51382pt too wide) in paragraph at lines 15--17 + $\OML/cmm/m/it/10 E \/cmr/m/n/10 =$ + [] + + +! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.16 W - e found the state space representation as: -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. +l.18 \begin{bmatrix} + +Your command was ignored. +Type I to replace it with another command, +or to continue without it. -Missing character: There is no W 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 u 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 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 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 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 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 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 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 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 a in font nullfont! -Missing character: There is no s in font nullfont! -Missing character: There is no : in font nullfont! +! 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. -Overfull \hbox (20.0pt too wide) in paragraph at lines 16--17 -[] - [] +! 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: Missing \begin{document}. +! LaTeX Error: There's no line here to end. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.18 Q - uestion 6) -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. +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 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 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 6 in font nullfont! -Missing character: There is no ) in font nullfont! +! 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. -Overfull \hbox (20.0pt too wide) in paragraph at lines 18--19 -[] +! 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{$x}'. In such cases +the way to recover is to insert both the forgotten and the +deleted material, e.g., by typing `I$}'. -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.20 O - n cherche un le pôle le plus dominant et on veut le mettre le plus à... - -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 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 r 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 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 e 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 l 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 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 d 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 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 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 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 u 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 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 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 l 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 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 g 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 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 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 d 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 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 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 d 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 y 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 i 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! -Missing character: There is no O 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 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 m 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 a 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 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 e 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 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 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 p in font nullfont! -Missing character: There is no o 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 e 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 u 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 o 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 n 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 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 ) in font nullfont! -Missing character: There is no . in font nullfont! - -Overfull \hbox (20.0pt too wide) in paragraph at lines 20--21 -[] - [] - - -Overfull \hbox (5.00002pt too wide) in paragraph at lines 20--21 -\/cmr/m/n/10 ^o - [] - - -Overfull \hbox (5.00002pt too wide) in paragraph at lines 20--21 -\/cmr/m/n/10 ^^Ra - [] - - -Overfull \hbox (4.44444pt too wide) in paragraph at lines 20--21 -\/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.23 Q - uestion 9) -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - -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 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 9 in font nullfont! -Missing character: There is no ) in font nullfont! -Missing character: There is no p in font nullfont! -Missing character: There is no h 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 m 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 d 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 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 / 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. -Overfull \hbox (20.0pt too wide) in paragraph at lines 23--25 -[] - [] +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. -Overfull \hbox (8.88889pt too wide) in paragraph at lines 23--25 -\/cmr/m/n/10 ^^Se^^Re - [] - - -Overfull \hbox (2.77779pt too wide) in paragraph at lines 23--25 -\/cmr/m/n/10 ' - [] - - -! LaTeX Error: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.26 Q - uestion 10 ) -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - -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 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 - 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. -! LaTeX Error: Unicode character   (U+202F) - not set up for use with LaTeX. +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.26 Question 10  - ) -You may provide a definition with -\DeclareUnicodeCharacter +l.23 \end{bmatrix} + +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! -Overfull \hbox (20.0pt too wide) in paragraph at lines 26--27 -[] +! 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} + +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.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} + +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}. + +See the LaTeX manual or LaTeX Companion for explanation. +Type H for immediate help. + ... + +l.53 \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 (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.28 \section +l.58 \section {Une autre section} The control sequence at the end of the top line of your error message was never \def'ed. If you have @@ -664,18 +1001,6 @@ 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: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.28 \section{U - ne autre section} -You're in trouble here. Try typing to proceed. -If that doesn't work, type X to quit. - 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! @@ -698,7 +1023,7 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.29 \begin{figure} +l.59 \begin{figure} [h] Your command was ignored. Type I to replace it with another command, @@ -708,7 +1033,7 @@ 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.31 \includegraphics +l.61 \includegraphics [width=0.5\textwidth]{example-image} % Remplacez pa... The control sequence at the end of the top line of your error message was never \def'ed. If you have @@ -729,7 +1054,7 @@ Missing character: There is no 5 in font nullfont! ! Missing number, treated as zero. ] -l.31 \includegraphics[width=0.5\textwidth] +l.61 \includegraphics[width=0.5\textwidth] {example-image} % Remplacez pa... A number should have been here; I inserted `0'. (If you can't figure out why I needed to see a number, @@ -738,7 +1063,7 @@ look up `weird error' in the index to The TeXbook.) ! Illegal unit of measure (pt inserted). ] -l.31 \includegraphics[width=0.5\textwidth] +l.61 \includegraphics[width=0.5\textwidth] {example-image} % Remplacez pa... 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! @@ -768,7 +1093,7 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.32 \caption +l.62 \caption {Ceci est un exemple de figure.} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. @@ -805,14 +1130,14 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.34 \end{figure} +l.64 \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 28--35 +Overfull \hbox (20.0pt too wide) in paragraph at lines 58--65 [] [] @@ -823,24 +1148,12 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.36 \begin{table} +l.66 \begin{table} [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.36 \begin{table}[ - 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! @@ -851,7 +1164,7 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.38 \caption +l.68 \caption {Ceci est un exemple de tableau.} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. @@ -882,10 +1195,6 @@ 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 . in font nullfont! -LaTeX Font Info: External font `cmex10' loaded for size -(Font) <7> on input line 39. -LaTeX Font Info: External font `cmex10' loaded for size -(Font) <5> on input line 39. Missing character: There is no C in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no l in font nullfont! @@ -953,24 +1262,24 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.46 \end{table} +l.76 \end{table} 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 36--47 +Overfull \hbox (20.0pt too wide) in paragraph at lines 66--77 [] [] -Overfull \hbox (13.33337pt too wide) in paragraph at lines 36--47 +Overfull \hbox (13.33337pt too wide) in paragraph at lines 66--77 [] [] ! Undefined control sequence. -l.48 \section +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 @@ -978,18 +1287,6 @@ 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: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.48 \section{A - nother section} -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 n in font nullfont! Missing character: There is no o in font nullfont! @@ -1005,7 +1302,7 @@ 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.49 \subsection +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 @@ -1028,7 +1325,7 @@ 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.50 \subsubsection +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 @@ -1070,7 +1367,7 @@ Missing character: There is no u in font nullfont! ! Undefined control sequence. \@footnotetext ...tins {\reset@font \footnotesize \interlinepenalty \interfo... -l.51 ...mpliqué\footnote{Une note de bas de page} +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 @@ -1081,7 +1378,7 @@ and I'll forget about whatever was undefined. ! Undefined control sequence. \@footnotetext ...}\color@begingroup \@makefntext {\rule \z@ \footnotesep \i... -l.51 ...mpliqué\footnote{Une note de bas de page} +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 @@ -1090,42 +1387,42 @@ 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 51--51 +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 51--51 +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 51--51 +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 51--51 +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 51--51 +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 51--51 +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 48--52 +Overfull \hbox (20.0pt too wide) in paragraph at lines 78--82 [] [] -Overfull \hbox (8.93057pt too wide) in paragraph at lines 48--52 +Overfull \hbox (8.93057pt too wide) in paragraph at lines 78--82 \/cmr/m/n/10 ^^Se[] [] @@ -1137,7 +1434,7 @@ See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... -l.53 \newpage +l.83 \newpage Your command was ignored. Type I to replace it with another command, @@ -1147,7 +1444,7 @@ or to continue without it. ! Undefined control sequence. \newlabel{fig:example}{{}{\thepage }{}{}{}} -l.53 \newpage +l.83 \newpage The control sequence at the end of the top line of your error message was never \def'ed. If you have @@ -1159,7 +1456,7 @@ and I'll forget about whatever was undefined. ! Undefined control sequence. \newlabel{tab:example}{{}{\thepage }{}{}{}} -l.53 \newpage +l.83 \newpage The control sequence at the end of the top line of your error message was never \def'ed. If you have @@ -1170,7 +1467,7 @@ and I'll forget about whatever was undefined. \newlabel{tab:example}{{}{}{}{}{}} ] ! Undefined control sequence. -l.54 \psection +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 @@ -1178,18 +1475,6 @@ 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: Missing \begin{document}. - -See the LaTeX manual or LaTeX Companion for explanation. -Type H for immediate help. - ... - -l.54 \psection{C - onclusion} -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 n in font nullfont! @@ -1221,11 +1506,11 @@ Missing character: There is no n in font nullfont! Here is how much of TeX's memory you used: - 44 strings out of 474222 - 789 string characters out of 5748733 - 1926975 words of memory out of 5000000 - 22396 multiletter control sequences out of 15000+600000 + 47 strings out of 474222 + 924 string characters out of 5748733 + 1929975 words of memory out of 5000000 + 22399 multiletter control sequences out of 15000+600000 558069 words of font info for 36 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 23i,7n,32p,224b,139s stack positions out of 10000i,1000n,20000p,200000b,200000s + 23i,7n,32p,149b,139s stack positions out of 10000i,1000n,20000p,200000b,200000s ! ==> Fatal error occurred, no output PDF file produced! diff --git a/latex/contents.tex b/latex/contents.tex index 5f3e90f..1ce6508 100644 --- a/latex/contents.tex +++ b/latex/contents.tex @@ -4,9 +4,16 @@ Une introduction \newpage \section{Dynamique du système avec équations differentielles partielles} \subsection{Espace d'état} -L'espace d'état se trouve sous la forme: +\textbf{Question 1} +L'espace d'état se trouve sous la forme: \begin{center} +\begin{equation} +\rho(\zeta)\frac{\partial^2 w}{\partial t^2}(\zeta,t) = -\frac{\partial^2}{\partial \zeta ^2}\begin{bmatrix} +EI(\zeta )\frac{\partial^2}{\partial \zeta^2}(\zeta,t) +\end{bmatrix} +-q(\zeta,t) +\end{equation} $E =$ \[ \begin{bmatrix} @@ -16,9 +23,47 @@ $E =$ -13/420 & -11/210 & -1/140 & 1/105 \end{bmatrix} \] -\end{center} +\begin{equation} +x_1(\zeta,t)=\frac{\partial^2 w}{\partial \zeta ^2}(\zeta,t) \; +x_2(\zeta,t)=\rho(\zeta)\frac{\partial w}{\partial t}(\zeta,t) +\end{equation} -Salut Thibo +\begin{equation} +e_1(\zeta,t)=EI(\zeta)x_1(\zeta,t) \; +e_2(\zeta,t)=\frac{1}{\rho(\zeta)}x_2(\zeta,t) +\end{equation} + +\begin{equation} +\dot{x}(t)=\begin{bmatrix} + +\dot{x}_1 \\ +\dot{x}_2 +\end{bmatrix} += \frac{\partial^2}{\partial z^2} +\begin{bmatrix} +0 & 1 \\ +-1 & 0 +\end{bmatrix} +\begin{bmatrix} +e_1(\zeta,t) & e_2(\zeta ,t) +\end{bmatrix} ++ +\begin{bmatrix} +0 \\ +-q(\zeta,t) +\end{bmatrix} +\end{equation} +\end{center} +Voici la represntation d'état à partir des equations diferentielles. + + +\textbf{Question 2} + + +Comment ajouter un image: + +\includegraphics[scale=1]{./Illustrations/im1.png} +Les Poles du système avec retour d'état. \section{Une autre section} \begin{figure}[h] diff --git a/latex/main.aux b/latex/main.aux index 9f7e89b..673e096 100644 --- a/latex/main.aux +++ b/latex/main.aux @@ -14,16 +14,16 @@ \@writefile{toc}{\contentsline {section}{Introduction}{1}{section*.1}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {1}Dynamique du système avec équations differentielles partielles}{2}{section.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Espace d'état}{2}{subsection.1.1}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}Une autre section}{2}{section.2}\protected@file@percent } -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Ceci est un exemple de figure.}}{2}{figure.1}\protected@file@percent } -\newlabel{fig:example}{{1}{2}{Ceci est un exemple de figure}{figure.1}{}} -\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Ceci est un exemple de tableau.}}{2}{table.1}\protected@file@percent } -\newlabel{tab:example}{{1}{2}{Ceci est un exemple de tableau}{table.1}{}} -\@writefile{toc}{\contentsline {section}{\numberline {3}Another section}{3}{section.3}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Une sous section}{3}{subsection.3.1}\protected@file@percent } -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Une sous sous section}{3}{subsubsection.3.1.1}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{Conclusion}{4}{section*.2}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {2}Une autre section}{3}{section.2}\protected@file@percent } +\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Ceci est un exemple de figure.}}{3}{figure.1}\protected@file@percent } +\newlabel{fig:example}{{1}{3}{Ceci est un exemple de figure}{figure.1}{}} +\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Ceci est un exemple de tableau.}}{4}{table.1}\protected@file@percent } +\newlabel{tab:example}{{1}{4}{Ceci est un exemple de tableau}{table.1}{}} +\@writefile{toc}{\contentsline {section}{\numberline {3}Another section}{4}{section.3}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Une sous section}{4}{subsection.3.1}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Une sous sous section}{4}{subsubsection.3.1.1}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{Conclusion}{5}{section*.2}\protected@file@percent } \global\mtcsecondpartfalse \pgfsyspdfmark {pgfid2}{6708151}{47648898} \abx@aux@read@bbl@mdfivesum{EE04F40F768DAEED26442158E95ABA61} -\gdef \@abspage@last{7} +\gdef \@abspage@last{8} diff --git a/latex/main.log b/latex/main.log index c69f74c..c1030b7 100644 --- a/latex/main.log +++ b/latex/main.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) 16 APR 2026 22:56 +This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 28 APR 2026 16:23 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -1231,39 +1231,59 @@ Package pdftex.def Info: template/assets/template_page.pdf used on input line 4. 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