
\documentclass[11pt]{book}

%packages yann
\usepackage{graphicx}
%\usepackage{index}    %%%%%%%%%%%%%%%%%%% INDEX UNIQUE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{multind}   
%%%%%%%%%%%%%%%%%%% INDEX MULTIPLES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% s'accompagne de multind.sty %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% explications dans le fichier netindex %%%%%%%%%%%
%\usepackage{amsmath}
\usepackage{epic,amsfonts,amssymb, isolatin1}
\usepackage{psfrag}
\usepackage[french]{babel}
%\usepackage{french}
\usepackage{subfigure}

%\newcommand{\nada}[1]{}
%Si on enlève [1], la commande n'agit pas.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\documentstyle[11pt,showidx]{book}
%\index{A}{water}
\textwidth 16cm \textheight 22.4cm \oddsidemargin -0.71cm \evensidemargin
-0.71cm \topmargin -0.6cm

%\input{macroo.tex}
%\input{Macro.tex}

%\input{macropict.tex}

%\pagestyle{plain}



%macros et autres yann
% ensembles Q R N Z C indicatrice polynomes
\gdef\PP{\hbox{\rm I\kern-.25em\hbox{P}}} \gdef\ind{\indi}

\gdef\RR{\hbox{\rm I\kern-.25em\hbox{R}}} \gdef\NN{\hbox{\rm
I\kern-.25em\hbox{N}}} \gdef\LLI{\hbox{\rm I\kern-.25em\hbox{L}}}
\gdef\ZZ{{\sl Z\hskip -1ex Z} } \gdef\CC{{\rm
\hbox{C\kern-.56em\raise.4ex
         \hbox{$\scriptscriptstyle |$}\kern+0.5 em }}}
\gdef\QQ{\rm \hbox{Q\kern-.35em\raise.4ex
         \hbox{$\scriptscriptstyle |$}\kern+0.5 em }}
% ensembles Q R N Z C indicatrice polynomes
\gdef\PP{\hbox{\rm I\kern-.25em\hbox{P}}} \gdef\ind{\indi}

\gdef\RR{{\hbox{\rm I\kern-.20em\hbox{R}}}} \gdef\NN{\hbox{\rm
I\kern-.25em\hbox{N}}} \gdef\LLI{\hbox{\rm I\kern-.25em\hbox{L}}}
\gdef\ZZ{{\sl Z\hskip -1ex Z} } \gdef\CC{\rm
\hbox{C\kern-.56em\raise.4ex
         \hbox{$\scriptscriptstyle |$}\kern+0.5 em }}
\gdef\QQ{\rm \hbox{Q\kern-.35em\raise.4ex
         \hbox{$\scriptscriptstyle |$}\kern+0.5 em }}
\newcommand \R {\RR}
\newcommand \Z {\ZZ}
\newcommand \N {\NN}

\newcommand \hu {\hat{u}}
\newcommand \tu {\tilde u}
\def\cqfd{\enddemo}     % fin de preuve
\newcommand{\indi}{{1\!\!1}}
\newcommand \com[1]{\fbox{\sf  #1}}
\newcommand \trait{
\noindent\noindent
\begin{picture}(454,5)(0,-5)
\drawline(0,2)(454,2)
\end{picture}}


%\def\R{é}sum{é}{\small\noindent\bf R{é}sum{é}. \rm}
\def\Abstract{\small\noindent\bf Abstract. \rm}

\def\nin{\not\in}                 % la negation de \in
\def\indic{1\!\!1}                % fonction indicatrice
\def\levelset{\chi}           % la surface de niveau
\def\meas{\mathop{\rm meas}}      % mesure de
\def\setB{\SetB}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\RR
\def\real{\RR}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\NN{I\!\!N}
\def\relative{{\ZZ}}

\def\complex{{\CC}}
\def\mes{\hbox{mes}}
\def\sin{\hbox{sin}}
\def\cos{\hbox{cos}}
\def\interieur{\hbox{\rm Int{é}rieur}}
\def\signe{\hbox{\rm Signe}}
\def\vect{\hbox{\rm Vect}}
\def\Re{\hbox{\rm Re}}
\def\support{\hbox{\rm Support}}
\def\supp{\hbox{\rm Support}}

\def\fb&{\begin{equation}}
\def\fe&{\end{equation}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ajouts sylvie
\newcommand{\ep}{\varepsilon}
\newcommand{\Om}{\Omega}
\newcommand{\om}{\omega}
\newcommand{\vfi}{\varphi}
\newcommand{\eps}{\varepsilon}
\newcommand{\psieps}{\psi_{\varepsilon}}
\newcommand{\psia}{\psi_{a}}
\newcommand{\grad}{\nabla}
\newcommand{\Ep}{E^{\prime}}
\newcommand{\vois}{{\cal V}(x)}
\newcommand{\lun}{{\ell}^1}
\newcommand{\linf}{{\ell}^{\infty}}
\newcommand{\Epp}{E^{\prime \prime}}
\newcommand{\Linf}{L^{\infty}}
\newcommand{\Di}{{\cal D}^{\prime}}
\newcommand{\cinf}{{\cal C}^{\infty}}
\newcommand{\ff}{\widehat{f}}
\newcommand{\DD}{{\cal D}}
\newcommand{\SLS}{{\cal S}}
\newcommand{\Lun}{L_{loc}^1}
\newcommand{\feps}{f_{\varepsilon}}
\newcommand{\Ld}{L^2(I)}
\newcommand{\Hun}{H^1(I)}
\newcommand{\Huno}{H^1(0,1)}
\newcommand{\Hnul}{H_0^1(I)}
\newcommand{\Hnulo}{H_0^1(0,1)}
\newcommand{\Abar}{\overline{A}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%rappel : \overline{cequ'onveut}
\newtheorem{thf}{Th\e or\ee me}[chapter]
\newtheorem{cor}{Corollaire}[chapter]
\newtheorem{pro}{Proposition}[chapter]
\newtheorem{Def}{D\e finition}[chapter]
\newtheorem{lem}{Lemme}[chapter]
\newtheorem{exa}{Exemple}[chapter]

\newtheorem{rem}{Remarque}[chapter]%  remarque
\def\drem{\begin{rem}\rm}%  sans
\def\frem{\end{rem}}%                   italique !

%\newtheorem{exo}{Exercice}[chapter]
\newtheorem{exo}{Exercice}
\def\dexo{\begin{exo}\rm}    %sans
\def\fexo{\end{exo}}        %italique !
\newtheorem{propr}{Propri\e t\e}[chapter]

%\newtheorem{Exer}{Exercice}[chapter]  %Exercice
\def\dexer{\dexo}    %sans
\def\fexer{\fexo}        %italique !

\def\quest{\vspace{0.25 cm} \noindent }
\def\subquest{\vspace{0.2cm}}

\newenvironment{Solution}[1]{{
\bf Solution #1 \newline  }} {  }
\def\dsolution{\begin{Solution}\small\it}
\def\fsolution{\end{Solution}\vspace{0.25 cm}}


\def\skipaline{\vspace{4 mm}\noindent}

\def\fb& {\begin{equation}}       % debut d'une equation
\def\fe& {\end{equation}}         % fin d'une equation
\def\enddemo{\hfill $\large\circ$ \newline\newline}     % fin de preuve
\def\Varphi{{\bf \varphi}}
\def\e {{é}}
\def\ee {{è}}
\def\eee {{\^e}}
\def\e {{é}}
\def\ea {{é} }
\def\ee {{è}}
\def\eee {{\^e}}
\def\a {{à} }
\def\aa {{\^a}}
\def\ii {{\^\i}}
\def\iii {{\"\i}}
\def\ccaadd{ c'est-{à}-dire }
\def\u {{\`u} }
\def\uu {{\^u}}
\def\oo {{\^o}}
\def\ooo {{\"o}}

%\newcommand\contentsname{Table des Matières}
%\newcommand\chaptername{Chapitre}
%\newcommand\today{\ifcase\month\or
%  Janvier\or F{é}vrier\or Mars\or Avril\or Mai\or Juin\or
%  Juillet\or Ao{\^u}t\or Septembre\or Octobre\or Novembre\or D{é}cembre\fi
%  \space\number\day, \number\year}


%rappel pour la cédille : fran\c cais
\def\indexentry#1#2{\noindent #1, #2 \newline}