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. **contents.tex (./contents.tex LaTeX2e <2023-11-01> patch level 1 L3 programming layer <2024-01-22> ! Undefined control sequence. l.1 \psection {Introduction} 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: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.1 \psection{I ntroduction} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. 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 r 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 u 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 e 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 r 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 u 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! Overfull \hbox (20.0pt too wide) in paragraph at lines 1--3 [] [] ! 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.4 \newpage Your command was ignored. Type I to replace it with another command, or to continue without it. [1] ! Undefined control sequence. l.5 \section {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 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.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 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 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. LaTeX Font Warning: Font shape `/cmr/m/n' undefined (Font) using `/cmr/m/n' instead on input line 5. ! 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 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 {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 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 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 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 (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 ^^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. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 10. ! LaTeX Error: Environment bmatrix undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... 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: \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 \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 ) [] 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.18 \begin{bmatrix} 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. 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} 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.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 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 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! ! LaTeX Error: Environment figure undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.59 \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.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 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 w 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 t in font nullfont! 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 number, treated as zero. ] 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, 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... 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.) 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 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 a in font nullfont! Missing character: There is no g 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.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. 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 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 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 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 r 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.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 58--65 [] [] ! LaTeX Error: Environment table undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.66 \begin{table} [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: \caption outside float. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... 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. 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 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 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 e 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 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 u 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 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 n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no 1 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 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 n 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 C 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 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 e in font nullfont! Missing character: There is no 3 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 n 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 1 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 n 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 2 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 n 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 3 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 n 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 4 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 n 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 5 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 n 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 6 in font nullfont! ! LaTeX Error: \begin{document} ended by \end{table}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... 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 66--77 [] [] Overfull \hbox (13.33337pt too wide) in paragraph at lines 66--77 [] [] ! 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! 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 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 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 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 m 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 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 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 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 [] [] Overfull \hbox (8.93057pt too wide) in paragraph at lines 78--82 \/cmr/m/n/10 ^^Se[] [] ! 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.83 \newpage 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 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. \newlabel{fig:example}{{}{}{}{}{}} ! Undefined control sequence. \newlabel{tab:example}{{}{\thepage }{}{}{}} l.83 \newpage 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. \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. 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 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 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 i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! ) ! Emergency stop. <*> contents.tex *** (job aborted, no legal \end found) Here is how much of TeX's memory you used: 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,149b,139s stack positions out of 10000i,1000n,20000p,200000b,200000s ! ==> Fatal error occurred, no output PDF file produced!