890 lines
34 KiB
Text
890 lines
34 KiB
Text
This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023/Debian) (preloaded format=pdflatex 2026.4.14) 7 MAY 2026 11:53
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entering extended mode
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**Q2.tex
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(./Q2.tex
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LaTeX2e <2023-11-01> patch level 1
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L3 programming layer <2024-01-22>
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See the LaTeX manual or LaTeX Companion for explanation.
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l.2 \textbf{Question 2}
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[]\OT1/cmr/bx/n/10 Question
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\OT1/cmr/bx/n/10 2
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l.4 À
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partir des informations données dans l'exercice, on peut écrire :
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LaTeX Font Info: Trying to load font information for +cmr on input line 4.
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LaTeX Font Info: No file cmr.fd. on input line 4.
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LaTeX Font Warning: Font shape `/cmr/m/n' undefined
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wrong@fontshape ...message {Corrupted NFSS tables}
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error@fontshape else let f...
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l.4 À
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partir des informations données dans l'exercice, on peut écrire :
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This error message was generated by an \errmessage
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command, so I can't give any explicit help.
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Pretend that you're Hercule Poirot: Examine all clues,
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and deduce the truth by order and method.
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LaTeX Font Warning: Font shape `/cmr/m/n' undefined
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[]\/cmr/m/n/10 ^^RA
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[]
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\/cmr/m/n/10 ^^Se
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\/cmr/m/n/10 ^^Se
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...
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l.6 \begin{equation}
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LaTeX Font Info: External font `cmex10' loaded for size
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LaTeX Font Info: External font `cmex10' loaded for size
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[] \/cmr/m/n/10 = [] = \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/
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cmr/m/n/10 )[][](\OML/cmm/m/it/10 t\/cmr/m/n/10 )
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[]
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! LaTeX Error: Missing \begin{document}.
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See the LaTeX manual or LaTeX Companion for explanation.
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Type H <return> for immediate help.
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...
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l.14 E
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n multipliant les deux membres par le vecteur d'approximation $\phi(\z...
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[]
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\OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )$
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[]
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! LaTeX Error: Missing \begin{document}.
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See the LaTeX manual or LaTeX Companion for explanation.
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Type H <return> for immediate help.
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...
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l.16 \begin{equation}
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You're in trouble here. Try typing <return> to proceed.
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[]
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[]
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\OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[] = \OML/c
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mm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/10
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^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[][](\OML/cmm/m/it/10 t\/cmr
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/m/n/10 )
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[]
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! LaTeX Error: Missing \begin{document}.
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Type H <return> for immediate help.
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...
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l.23 E
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n remplaçant ensuite $e_2$ par son approximation, on obtient :
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\/cmr/m/n/10 ^^Xc
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\OML/cmm/m/it/10 e[]$
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...
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l.25 \begin{equation}
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\OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[] [] = \OM
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L/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/cmm/m/it/
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10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[][](\OML/cmm/m/it/10 t\/
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cmr/m/n/10 )
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! LaTeX Error: Missing \begin{document}.
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...
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l.35 C
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omme $e_{2d}(t)$ ne dépend pas de $\zeta$, il peut être sorti de l'i...
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\OML/cmm/m/it/10 e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )$
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[]
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\OML/cmm/m/it/10 ^^P$
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\/cmr/m/n/10 ^e
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\/cmr/m/n/10 [0\OML/cmm/m/it/10 ; L\/cmr/m/n/10 ]$
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[]
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Overfull \hbox (227.13411pt too wide) detected at line 47
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[][] \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )\OML/c
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mm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[] \OML/cmm/m/it/
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10 d^^P []\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = [][] \OML/cmm/m/it/1
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0 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 ^^P\/cmr/m/n/10 )[] \OML/cmm/m/it/10 d^^P e
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[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )
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[]
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! LaTeX Error: Missing \begin{document}.
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See the LaTeX manual or LaTeX Companion for explanation.
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Type H <return> for immediate help.
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...
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l.49 A
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près avoir fait une integration par partie:
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You're in trouble here. Try typing <return> to proceed.
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If that doesn't work, type X <return> to quit.
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Missing character: There is no A in font nullfont!
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Overfull \hbox (24.44444pt too wide) in paragraph at lines 49--50
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[]\/cmr/m/n/10 ^^Re
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[]
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! LaTeX Error: Missing \begin{document}.
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See the LaTeX manual or LaTeX Companion for explanation.
|
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Type H <return> for immediate help.
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...
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l.53 O
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n identifie alors les matrices $E$ et $D$. Ainsi, les deux équations ...
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You're in trouble here. Try typing <return> to proceed.
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If that doesn't work, type X <return> to quit.
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Missing character: There is no O in font nullfont!
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Missing character: There is no n in font nullfont!
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Missing character: There is no i in font nullfont!
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Missing character: There is no d in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no n in font nullfont!
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Missing character: There is no t in font nullfont!
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Missing character: There is no i in font nullfont!
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Missing character: There is no f in font nullfont!
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Missing character: There is no i in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no a in font nullfont!
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Missing character: There is no l in font nullfont!
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Missing character: There is no o in font nullfont!
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Missing character: There is no r in font nullfont!
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Missing character: There is no s in font nullfont!
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Missing character: There is no l in font nullfont!
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Missing character: There is no m in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no d in font nullfont!
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Missing character: There is no ' in font nullfont!
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Missing character: There is no t in font nullfont!
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Missing character: There is no a in font nullfont!
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Missing character: There is no t in font nullfont!
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Missing character: There is no d in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no s in font nullfont!
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Missing character: There is no s in font nullfont!
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Missing character: There is no ' in font nullfont!
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Missing character: There is no c in font nullfont!
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Missing character: There is no r in font nullfont!
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Missing character: There is no i in font nullfont!
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Missing character: There is no v in font nullfont!
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Missing character: There is no e in font nullfont!
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Missing character: There is no t in font nullfont!
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Missing character: There is no : in font nullfont!
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Overfull \hbox (20.0pt too wide) in paragraph at lines 53--54
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[]
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[]
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Overfull \hbox (7.95831pt too wide) in paragraph at lines 53--54
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\OML/cmm/m/it/10 E$
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[]
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Overfull \hbox (8.55695pt too wide) in paragraph at lines 53--54
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\OML/cmm/m/it/10 D$
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[]
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Overfull \hbox (4.44444pt too wide) in paragraph at lines 53--54
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\/cmr/m/n/10 ^^Se
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[]
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Overfull \hbox (4.44444pt too wide) in paragraph at lines 53--54
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\/cmr/m/n/10 ^^Se
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[]
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Overfull \hbox (8.88889pt too wide) in paragraph at lines 53--54
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\/cmr/m/n/10 ^^Se^^Se
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[]
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Overfull \hbox (4.44444pt too wide) in paragraph at lines 53--54
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\/cmr/m/n/10 ^^Se
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[]
|
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|
! LaTeX Error: Missing \begin{document}.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
|
|
|
l.55 \begin{equation}
|
|
|
|
You're in trouble here. Try typing <return> to proceed.
|
|
If that doesn't work, type X <return> to quit.
|
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|
|
Overfull \hbox (20.0pt too wide) in paragraph at lines 55--55
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[]
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[]
|
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! LaTeX Error: Environment aligned undefined.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
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|
|
l.56 \begin{aligned}
|
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|
|
Your command was ignored.
|
|
Type I <command> <return> to replace it with another command,
|
|
or <return> to continue without it.
|
|
|
|
! Misplaced alignment tab character &.
|
|
l.57 E\dot{x}_{1d}(t) &
|
|
= D e_{2d}(t),\\
|
|
I can't figure out why you would want to use a tab mark
|
|
here. If you just want an ampersand, the remedy is
|
|
simple: Just type `I\&' now. But if some right brace
|
|
up above has ended a previous alignment prematurely,
|
|
you're probably due for more error messages, and you
|
|
might try typing `S' now just to see what is salvageable.
|
|
|
|
! Misplaced alignment tab character &.
|
|
l.58 E\dot{x}_{2d}(t) &
|
|
= -D^T e_{1d}(t)-\phi(L)u(t)-F_{ext}.
|
|
I can't figure out why you would want to use a tab mark
|
|
here. If you just want an ampersand, the remedy is
|
|
simple: Just type `I\&' now. But if some right brace
|
|
up above has ended a previous alignment prematurely,
|
|
you're probably due for more error messages, and you
|
|
might try typing `S' now just to see what is salvageable.
|
|
|
|
|
|
! LaTeX Error: \begin{equation} on input line 55 ended by \end{aligned}.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
|
|
|
l.59 \end{aligned}
|
|
|
|
Your command was ignored.
|
|
Type I <command> <return> to replace it with another command,
|
|
or <return> to continue without it.
|
|
|
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|
|
Overfull \hbox (253.38242pt too wide) detected at line 60
|
|
\OML/cmm/m/it/10 E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OML/cmm/m
|
|
/it/10 De[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 )\OML/cmm/m/it/10 ; []
|
|
E[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) = \OMS/cmsy/m/n/10 ^^@\OML/cm
|
|
m/m/it/10 D[]e[]\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10
|
|
^^@ \OML/cmm/m/it/10 ^^^\/cmr/m/n/10 (\OML/cmm/m/it/10 L\/cmr/m/n/10 )\OML/cmm
|
|
/m/it/10 u\/cmr/m/n/10 (\OML/cmm/m/it/10 t\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^@ \
|
|
OML/cmm/m/it/10 F[]:
|
|
[]
|
|
|
|
|
|
! LaTeX Error: Missing \begin{document}.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
|
|
|
l.62 E
|
|
nfin, on obtient :
|
|
You're in trouble here. Try typing <return> to proceed.
|
|
If that doesn't work, type X <return> to quit.
|
|
|
|
Missing character: There is no E in font nullfont!
|
|
Missing character: There is no n in font nullfont!
|
|
Missing character: There is no f in font nullfont!
|
|
Missing character: There is no i in font nullfont!
|
|
Missing character: There is no n in font nullfont!
|
|
Missing character: There is no , in font nullfont!
|
|
Missing character: There is no o in font nullfont!
|
|
Missing character: There is no n in font nullfont!
|
|
Missing character: There is no o in font nullfont!
|
|
Missing character: There is no b in font nullfont!
|
|
Missing character: There is no t in font nullfont!
|
|
Missing character: There is no i in font nullfont!
|
|
Missing character: There is no e in font nullfont!
|
|
Missing character: There is no n in font nullfont!
|
|
Missing character: There is no t in font nullfont!
|
|
Missing character: There is no : in font nullfont!
|
|
|
|
Overfull \hbox (20.0pt too wide) in paragraph at lines 62--63
|
|
[]
|
|
[]
|
|
|
|
|
|
! LaTeX Error: Missing \begin{document}.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
|
|
|
l.64 \begin{equation}
|
|
|
|
You're in trouble here. Try typing <return> to proceed.
|
|
If that doesn't work, type X <return> to quit.
|
|
|
|
|
|
Overfull \hbox (20.0pt too wide) in paragraph at lines 64--64
|
|
[]
|
|
[]
|
|
|
|
! Undefined control sequence.
|
|
l.65 \boxed
|
|
{
|
|
The control sequence at the end of the top line
|
|
of your error message was never \def'ed. If you have
|
|
misspelled it (e.g., `\hobx'), type `I' and the correct
|
|
spelling (e.g., `I\hbox'). Otherwise just continue,
|
|
and I'll forget about whatever was undefined.
|
|
|
|
|
|
! LaTeX Error: Environment aligned undefined.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
|
|
|
l.66 \begin{aligned}
|
|
|
|
Your command was ignored.
|
|
Type I <command> <return> to replace it with another command,
|
|
or <return> to continue without it.
|
|
|
|
! Misplaced alignment tab character &.
|
|
l.67 E\dot{x}_{1d}(t) &
|
|
= D e_{2d}(t),\\
|
|
I can't figure out why you would want to use a tab mark
|
|
here. If you just want an ampersand, the remedy is
|
|
simple: Just type `I\&' now. But if some right brace
|
|
up above has ended a previous alignment prematurely,
|
|
you're probably due for more error messages, and you
|
|
might try typing `S' now just to see what is salvageable.
|
|
|
|
! Misplaced alignment tab character &.
|
|
l.68 E\dot{x}_{2d}(t) &
|
|
= -D^T e_{1d}(t)-\phi(L)u(t)-F_{ext},\\
|
|
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.69 y(t) &
|
|
= -\phi(L)^T e_{2d}(t).
|
|
I can't figure out why you would want to use a tab mark
|
|
here. If you just want an ampersand, the remedy is
|
|
simple: Just type `I\&' now. But if some right brace
|
|
up above has ended a previous alignment prematurely,
|
|
you're probably due for more error messages, and you
|
|
might try typing `S' now just to see what is salvageable.
|
|
|
|
|
|
! LaTeX Error: \begin{equation} on input line 64 ended by \end{aligned}.
|
|
|
|
See the LaTeX manual or LaTeX Companion for explanation.
|
|
Type H <return> for immediate help.
|
|
...
|
|
|
|
l.70 \end{aligned}
|
|
|
|
Your command was ignored.
|
|
Type I <command> <return> to replace it with another command,
|
|
or <return> to continue without it.
|
|
|
|
|
|
Overfull \hbox (356.01259pt too wide) detected at line 72
|
|
[]
|
|
[]
|
|
|
|
)
|
|
! Emergency stop.
|
|
<*> Q2.tex
|
|
|
|
*** (job aborted, no legal \end found)
|
|
|
|
|
|
Here is how much of TeX's memory you used:
|
|
41 strings out of 474222
|
|
714 string characters out of 5748733
|
|
1925975 words of memory out of 5000000
|
|
22394 multiletter control sequences out of 15000+600000
|
|
558377 words of font info for 37 fonts, out of 8000000 for 9000
|
|
1141 hyphenation exceptions out of 8191
|
|
23i,3n,32p,163b,91s stack positions out of 10000i,1000n,20000p,200000b,200000s
|
|
! ==> Fatal error occurred, no output PDF file produced!
|