% Jean-Pierre Demailly
% Universit\'e de Grenoble I, Institut Fourier
% \'Equations Diff\'erentielles et Analyse Num\'erique
% Collection Grenoble-Sciences, Presses Universitaires de Grenoble
% Fichier de Macros Plain-TeX

% \input accents.tex

% page setting
\magnification=1000
\pretolerance=500 \tolerance=1000 \brokenpenalty=5000
\hsize=12.7cm
\vsize=20.4cm
\hoffset=2mm
\parskip3pt plus 1pt
\topskip=18pt
\parindent=0.0cm

% new fonts definitions
\font\seventeenrm=cmr10 at 17.28pt
\font\seventeenbf=cmbx10 at 17.28pt
\font\seventeenbfit=cmmib10 at 17.28pt
\font\seventeenbsy=cmbsy10 at 17.28pt
\font\seventeenbxsl=cmbxsl10 at 17.28pt
\font\seventeenbzsc=cmbzsc10 at 17.28pt
\font\fourteenbf=cmbx10 at 14.4pt
\font\fourteenbfit=cmmib10 at 14.4pt
\font\fourteenbsy=cmbsy10 at 14.4pt
\font\fourteenbxsl=cmbxsl10 at 14.4pt
\font\fourteenbzsc=cmbzsc10 at 14.4pt
\font\twelvei=cmmi10 at 12pt
\font\twelvebf=cmbx10 at 12pt
\font\twelvebfit=cmmib10 at 12pt
\font\twelverm=cmr10 at 12pt
\font\twelvesy=cmsy10 at 12pt
\font\twelvebsy=cmbsy10 at 12pt
\font\twelvebxsl=cmbxsl10 at 12pt
\font\twelvebzsc=cmbzsc10 at 12pt
\font\twelveline=line10 at 12pt

\font\elevenbf=cmbx10 at 10.9545pt
\font\elevenbxti=cmbxti10 at 10.9545pt
\font\elevenbfit=cmmib10 at 10.9545pt
\font\elevenbsy=cmbsy10 at 10.9545pt

\font\sc=cmcsc10
\font\bzsc=cmbzsc10
\font\tenline=line10
\font\tenbsy=cmbsy10
\font\eightbsy=cmbsy8
\font\sevenbsy=cmbsy7
\font\sixbsy=cmbsy6
\font\fivebsy=cmbsy5
\newfam\bsyfam
  \textfont\bsyfam=\tenbsy
  \scriptfont\bsyfam=\sevenbsy
  \scriptscriptfont\bsyfam=\fivebsy
\def\bsy{\fam\bsyfam\tenbsy}

\font\fourteenCal=eusm10 at 14.4pt
\font\twelveCal=eusm10 at 12pt
\font\elevenCal=eusm10 at 10.9545pt
\font\tenCal=eusm10
\font\sevenCal=eusm7
\font\fiveCal=eusm5
\newfam\Calfam
  \textfont\Calfam=\tenCal
  \scriptfont\Calfam=\sevenCal
  \scriptscriptfont\Calfam=\fiveCal
\def\Cal{\fam\Calfam\tenCal}

\font\fourteenmsa=msam10 at 14.4pt
\font\twelvemsa=msam10 at 12pt
\font\elevenmsa=msam10 at 10.9545pt
\font\tenmsa=msam10
\font\sevenmsa=msam7
\font\fivemsa=msam5
\newfam\msafam
  \textfont\msafam=\tenmsa
  \scriptfont\msafam=\sevenmsa
  \scriptscriptfont\msafam=\fivemsa
\def\msa{\fam\msafam\tenmsa}

\font\fourteenmsb=msbm10 at 14.4pt
\font\twelvemsb=msbm10 at 12pt
\font\elevenmsb=msbm10 at 10.9545pt
\font\tenmsb=msbm10
\font\sevenmsb=msbm7
\font\fivemsb=msbm5
\newfam\msbfam
  \textfont\msbfam=\tenmsb
  \scriptfont\msbfam=\sevenmsb
  \scriptscriptfont\msbfam=\fivemsb
\def\Bbb{\fam\msbfam\tenmsb}

\font\tenbfit=cmmib10
\font\eightbfit=cmmib8
\font\sevenbfit=cmmib7
\font\sixbfit=cmmib6
\font\fivebfit=cmmib5
\newfam\bfitfam
  \textfont\bfitfam=\tenbfit
  \scriptfont\bfitfam=\sevenbfit
  \scriptscriptfont\bfitfam=\fivebfit
\def\bfit{\fam\bfitfam\tenbfit}

\font\eightrm=cmr8
\font\eighti=cmmi8
\font\eightsy=cmsy8
\font\eightbf=cmbx8
\font\eighttt=cmtt8
\font\eightit=cmti8
\font\eightsl=cmsl8
\font\eightmsa=msam8
\font\eightmsb=msbm8
\font\sixrm=cmr6
\font\sixi=cmmi6
\font\sixsy=cmsy6
\font\sixbf=cmbx6

% changing font sizes

\catcode`\@=11
\def\eightpoint{%
  \textfont0=\eightrm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm
  \def\rm{\fam\z@\eightrm}%
  \textfont1=\eighti \scriptfont1=\sixi \scriptscriptfont1=\fivei
  \def\oldstyle{\fam\@ne\eighti}%
  \textfont2=\eightsy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy
  \textfont\itfam=\eightit
  \def\it{\fam\itfam\eightit}%
  \textfont\slfam=\eightsl
  \def\sl{\fam\slfam\eightsl}%
  \textfont\bffam=\eightbf \scriptfont\bffam=\sixbf
  \scriptscriptfont\bffam=\fivebf
  \def\bf{\fam\bffam\eightbf}%
  \textfont\ttfam=\eighttt
  \def\tt{\fam\ttfam\eighttt}%
  \textfont\msbfam=\eightmsb
  \def\Bbb{\fam\msbfam\eightmsb}%
  \font\sc=cmcsc8
  \abovedisplayskip=9pt plus 2pt minus 6pt
  \abovedisplayshortskip=0pt plus 2pt
  \belowdisplayskip=9pt plus 2pt minus 6pt
  \belowdisplayshortskip=5pt plus 2pt minus 3pt
  \smallskipamount=2pt plus 1pt minus 1pt
  \medskipamount=4pt plus 2pt minus 1pt
  \bigskipamount=9pt plus 3pt minus 3pt
  \normalbaselineskip=9pt
  \setbox\strutbox=\hbox{\vrule height7pt depth2pt width0pt}%
  \let\bigf@ntpc=\eightrm \let\smallf@ntpc=\sixrm
  \normalbaselines\rm}

\def\seventeenpointbf{%
 \textfont0=\seventeenbf  \scriptfont0=\twelvebf  \scriptscriptfont0=\eightbf
 \textfont1=\seventeenbfit\scriptfont1=\twelvebfit\scriptscriptfont1=\eightbfit
 \textfont2=\seventeenbsy \scriptfont2=\twelvebsy \scriptscriptfont2=\eightbsy
 \seventeenbzsc
 \normalbaselineskip=20.736pt\normalbaselines}

\def\fourteenpointbf{%
 \textfont0=\fourteenbf   \scriptfont0=\tenbf   \scriptscriptfont0=\sevenbf
 \textfont1=\fourteenbfit \scriptfont1=\tenbfit \scriptscriptfont1=\sevenbfit
 \textfont2=\fourteenbsy  \scriptfont2=\tenbsy  \scriptscriptfont2=\sevenbsy
 \textfont\msafam=\fourteenmsa \textfont\msbfam=\fourteenmsb    
 \textfont\Calfam=\fourteenCal
 \fourteenbzsc
 \normalbaselineskip=17.28pt\normalbaselines}

\def\twelvepointbf{%
 \textfont0=\twelvebf   \scriptfont0=\eightbf   \scriptscriptfont0=\sixbf
 \textfont1=\twelvebfit \scriptfont1=\eightbfit \scriptscriptfont1=\sixbfit
 \textfont2=\twelvebsy  \scriptfont2=\eightbsy  \scriptscriptfont2=\sixbsy
 \textfont\msafam=\twelvemsa \textfont\msbfam=\twelvemsb   
 \textfont\Calfam=\twelveCal
 \twelvebzsc
 \normalbaselineskip=14.4pt\normalbaselines}

\def\elevenpointbf{%
 \textfont0=\elevenbf   \scriptfont0=\eightbf   \scriptscriptfont0=\sixbf
 \textfont1=\elevenbfit \scriptfont1=\eightbfit \scriptscriptfont1=\sixbfit
 \textfont2=\elevenbsy  \scriptfont2=\eightbsy  \scriptscriptfont2=\sixbsy
 \textfont\msafam=\elevenmsa \textfont\msbfam=\elevenmsb   
 \textfont\Calfam=\elevenCal
 \elevenbxti}

\def\tenpointbf{%
 \textfont0=\tenbf   \scriptfont0=\sevenbf   \scriptscriptfont0=\fivebf
 \textfont1=\tenbfit \scriptfont1=\sevenbfit \scriptscriptfont1=\fivebfit
 \textfont2=\tenbsy  \scriptfont2=\sevenbsy  \scriptscriptfont2=\fivebsy
 \textfont\msafam=\tenmsa \textfont\msbfam=\tenmsb   
 \textfont\Calfam=\tenCal
 \tenbf}
        
% main item macros

\def\sect#1{\noindent\phantom{}\kern12mm\llap{\hbox{#1.}}\kern1mm}
\def\NUMPAGE#1{~\dotfill\hbox to8mm{\hfil#1}}
\def\NONUMPAGE#1{~\dotfill\hbox to8mm{\hfil ???}}

\def\outputwarning{%
\message{^^JATTENTION\string: il faudra relancer TeX une seconde fois
pour obtenir une table des matieres correctement paginee !!^^J}}

\newcount\auxexiste
\def\openauxfile{\immediate\openin1=equadif.aux
\ifeof1
\outputwarning
\let\numpage=\NONUMPAGE
\auxexiste=0
\else
\let\numpage=\NUMPAGE
\auxexiste=1
\input equadif.aux
\fi
\immediate\closeout1
\immediate\openout1=equadif.aux
}

\def\auxwarning{%
\immediate\closeout1
\ifnum\auxexiste=0
\outputwarning
\fi
}

\let\prem=\bf

\def\bottomnote#1#2{\footnote{${}^{#1}$}{{\eightpoint#2}}}
\newbox\booktitlebox   \setbox\booktitlebox\hbox{\hfil}
\newbox\chaptitlebox   \setbox\chaptitlebox\hbox{\hfil}
\newcount\fst \fst=1
\def\folio{\ifnum\pageno=\fst{\hfil}\else
  \ifodd\pageno{{\eightpoint\copy\chaptitlebox}\hfil\number\pageno}%
  \else{\number\pageno\hfil{\eightpoint\copy\booktitlebox}}\fi\fi}
\footline={\hfil}
\headline={\folio} 
       
\def\CHpage{
   \immediate\write1{\string\def\string\CH \romannumeral\numberchap\string{%
   \number\pageno\string}}}

\def\pagejump{
  \vfill\eject
  \ifodd\pageno \else {\headline={\hfil}\null\vskip0pt\vfill\eject} \fi
  \fst=\pageno
  \numbersection=0
  \advance\numberchap by 1
  \CHpage}

\def\blankline{\phantom{}\hfil\vskip0pt}
\def\booktitlerunning#1|{\setbox\booktitlebox\hbox{\eightpoint\sc #1}}
\def\chaptitlerunning#1|{\setbox\chaptitlebox\hbox{\eightpoint\sc #1}}
\def\chtitle#1|{\noindent\hfil{\seventeenpointbf #1}}
\def\title#1|{\noindent\hfil$\smash{\hbox{\seventeenpointbf #1}}$\hfil
              \chaptitlerunning #1|\medskip}
\def\titleleft#1|{\noindent$\smash{\hbox{\seventeenpointbf #1}}$\hfil
              \chaptitlerunning #1|\medskip}

\newcount\numbersection \numbersection=-10000
\newcount\numberchap \numberchap=-1

\def\Spage{\immediate\write1{\string\def 
  \string\CH \romannumeral\numberchap
  S\romannumeral\numbersection\string{%
  \number\pageno \string}}}

\def\section#1 #2|{\setbox3\hbox{\fourteenbzsc #1\ }
  \vskip1cm\penalty -100 
  \vbox{\baselineskip=17.28pt\noindent
  {\raggedright\hangindent\wd3\hangafter1{\fourteenpointbf 
  \copy3\ignorespaces#2\vskip0pt}}}
  \penalty 500
  \vskip8pt
  \advance\numbersection by 1
  \ifnum\numbersection>-1000 \Spage \fi}

\def\subsection#1 #2|{\setbox3\hbox{\twelvebzsc #1\ }
  \removelastskip
  \vskip0.6cm\penalty -100
  \vbox{\baselineskip=14.4pt\noindent
  {\raggedright\hangindent\wd3\hangafter1{\twelvepointbf 
  \copy3\ignorespaces#2\vskip0pt}}}
  \penalty 500
  \vskip3pt}

\def\bib#1&#2&{\hangindent=7mm\hangafter=1\noindent{\sc #1}\ {\rm #2.}\par}
  
\catcode`@=11    
\def\cmalign#1{\null\,\vcenter{\normalbaselines\m@th
    \ialign{\hfil$##$&&$##$\hfil\crcr
      \mathstrut\crcr\noalign{\kern-\baselineskip}
      #1\crcr\mathstrut\crcr\noalign{\kern-\baselineskip}}}\,}
\catcode`@=12

\def\boxit#1#2{\hbox{\vrule
 \vbox{\hrule\kern#1
  \vtop{\hbox{\kern#1 #2\kern#1}%
   \kern#1\hrule}}%
 \vrule}}
\def\boxmat#1#2{\boxit{#1}{$#2$}} 

\def\state#1|{\noindent{\elevenpointbf #1}}

\def\today{\ifcase\month\or
January\or February\or March\or April\or May\or June\or July\or August\or
September\or October\or November\or December\fi\ \number\day, \number\year}

\def\aujourdhui{\number\day\ \ifcase\month\or
janvier\or f\'evrier\or mars\or avril\or mai\or juin\or juillet\or ao\^ut\or
septembre\or octobre\or novembre\or d\'ecembre\fi\ \number\year}

\def\bibitem#1&#2&#3&#4&%
{\hangindent=1.66cm\hangafter=1
\noindent\rlap{\hbox{\bf #1}}\kern1.66cm{\rm #2}{\sl #3}{\rm #4.}} 

\newdimen\dpp
\long\def\majdeb#1\majfin{\setbox0\vbox{#1} \dpp=3pt \advance\dpp by \dp0
\hbox{\kern-4mm\vrule height\ht0 depth\dpp width1mm\kern3mm\copy0}}
\long\def\majedeb#1\majefin{\setbox0\vbox{#1} \dpp=3pt \advance\dpp by \dp0
\hbox{\kern-4mm
      \vrule height\ht0 depth\dpp width0.4pt
      \kern0.4mm
      \vrule height\ht0 depth\dpp width0.4pt
      \kern3mm\copy0}}

% inclusion of PostScript files
\special{header=oldlib.eps}
\long\def\InsertFig#1 #2 #3 #4\EndFig{\par
\hbox{\hskip #1mm$\vbox to#2mm{\vfil\special{" 
%(oldlib.eps) run
#3}}#4$}}
\long\def\InsertFigFile#1 #2 #3 #4\EndFig{\par
\hbox{\hskip #1mm$\vbox to#2mm{\vfil\special{psfile= #3}}#4$}}
\long\def\LabelTeX#1 #2 #3\ELTX{\rlap{\kern#1mm\raise#2mm\hbox{#3}}}
      
% blackboard symbols
\def\bC{{\Bbb C}}
\def\bK{{\Bbb K}}
\def\bN{{\Bbb N}}
\def\bQ{{\Bbb Q}}
\def\bR{{\Bbb R}}
\def\bZ{{\Bbb Z}}
\def\bone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}

% calligraphic symbols
\def\cA{{\Cal A}}
%\def\cB{{\Cal B}}
\def\cC{{\Cal C}}
\def\cD{{\Cal D}}
%\def\cE{{\Cal E}}
\def\cF{{\Cal F}}
%\def\cG{{\Cal G}}
%\def\cH{{\Cal H}}
\def\cI{{\Cal I}}
%\def\cJ{{\Cal J}}
%\def\cK{{\Cal K}}
\def\cL{{\Cal L}}
%\def\cM{{\Cal M}}
\def\cN{{\Cal N}}
%\def\cO{{\Cal O}}
\def\cP{{\Cal P}}
%\def\cQ{{\Cal Q}}
%\def\cR{{\Cal R}}
\def\cS{{\Cal S}}
%\def\cT{{\Cal T}}
%\def\cU{{\Cal U}}
%\def\cV{{\Cal V}}
%\def\cW{{\Cal W}}
%\def\cX{{\Cal X}}
%\def\cY{{\Cal Y}}
%\def\cZ{{\Cal Z}}

% special symbols
\def\ii{{\rm i}}
\def\ee{{\rm e}}
\def\numero{n${}^\circ\,$}
\def\newline{\hfill\break}
\def\ld{,\,\ldots\,,}
\def\bu{{\scriptstyle\bullet}}
\def\bigzero{\hbox{~\seventeenrm 0~~~}}
\def\blacksquare{\hbox{\vrule height 1.453ex  width 1.453ex  depth 0ex}}
\def\branch{\raise2pt\hbox{
   \vbox{\hbox{\vrule height 0.4pt depth 0pt width 12.2pt}
         \hbox{\raise-11.6pt\hbox{\twelveline\char"00}}}}}
\def\og{\hbox{$\raise1pt\hbox{$\scriptscriptstyle\langle\!\langle$}$}}
\def\fg{\hbox{$\kern1pt\raise1pt\hbox{$\scriptscriptstyle\rangle\!\rangle$}$}}
\def\tvi{{\vrule height 10pt depth 5pt width 0pt}}
\def\tv{\tvi\vrule}
\def\hexnbr#1{\ifnum#1<10 \number#1\else
 \ifnum#1=10 A\else\ifnum#1=11 B\else\ifnum#1=12 C\else
 \ifnum#1=13 D\else\ifnum#1=14 E\else\ifnum#1=15 F\fi\fi\fi\fi\fi\fi\fi}
\def\msatype{\hexnbr\msafam}
\def\msbtype{\hexnbr\msbfam}
\mathchardef\restr="3\msatype16
\mathchardef\supsetneqq="3\msbtype25
\mathchardef\ssm="2\msbtype72
\mathchardef\compl="0\msatype7B
\mathchardef\subsetneq="3\msbtype28
\mathchardef\supsetneq="3\msbtype29

% displaystyles, hats and tildes and over/underlines
\let\disp=\displaystyle
\let\scrip=\scriptstyle
\let\mil=\,
\let\ol=\overline
\let\ul=\underline
\let\wt=\widetilde
\let\wh=\widehat
\def\build#1|#2|#3|{\mathrel{\mathop{\null#1}\limits^{#2}_{#3}}}
\def\frac#1#2{{#1\over#2}}
\def\dfrac#1#2{{#1\over#2}}
%\def\dfrac#1#2{{\displaystyle{#1\over#2}}}
\def\fracs#1#2{{\scriptstyle{#1\over#2}}}
\def\fracss#1#2{{\scriptscriptstyle{#1\over#2}}}
\def\boxit#1#2{\hbox{\vrule
 \vbox{\hrule\kern#1
  \vtop{\hbox{\kern#1 #2\kern#1}%
   \kern#1\hrule}}%
 \vrule}}
\def\boxmat#1#2{\boxit{#1}{$#2$}} 

% arrows
\def\bignearrow{\hbox{\twelvesy\char"25}}
\def\bigsearrow{\hbox{\twelvesy\char"26}}
\def\bignwarrow{\hbox{\twelvesy\char"2D}}
\def\bigswarrow{\hbox{\twelvesy\char"2E}}
\let\lmapsto=\longmapsto
\let\lra=\longrightarrow
\let\Lra=\Longrightarrow
\def\lhra{\mathrel{\lhook\joinrel\longrightarrow}}
\def\vlra#1|{\mathrel{\hbox to#1mm{\rightarrowfill}}}
\def\vlhra#1|{\mathrel{\lhook\joinrel\hbox to#1mm{\rightarrowfill}}}
\let\Llra=\Longleftrightarrow
\def\VVert{{|}\kern-1.2pt{|}\kern-1.2pt{|}}

% mathematical operators
\def\Re{\mathop{\rm Re}\nolimits}
\def\Im{\mathop{\rm Im}\nolimits}
\def\Id{\mathop{\rm Id}\nolimits}
\def\Ker{\mathop{\rm Ker}\nolimits}
\def\Hom{\mathop{\rm Hom}\nolimits}
\def\End{\mathop{\rm End}\nolimits}
\def\codim{\mathop{\rm codim}\nolimits}
\def\cotan{\mathop{\rm cotan}\nolimits}
\def\grad{\mathop{\rm grad}\nolimits}
\def\Log{\mathop{\rm Log}\nolimits}
\def\Arccos{\mathop{{\rm Arc}\,{\rm cos}}\nolimits}
\def\Arcsin{\mathop{{\rm Arc}\,{\rm sin}}\nolimits}
\def\Argcosh{\mathop{{\rm Arg}\,{\rm cosh}}\nolimits}
\def\Argsinh{\mathop{{\rm Arg}\,{\rm sinh}}\nolimits}
\def\tr{\mathop{\rm tr}\nolimits}
\def\lg{\mathop{\rm long}\nolimits}
\def\Sup{\mathop{\rm Sup}\nolimits}
\def\rmC{\hbox{\rm C}}
\def\rmE{\hbox{\rm E}}
\def\pf{p\kern-1pt f}

% Running title

\booktitlerunning Analyse num\'erique et \'equations diff\'erentielles|

