$ \newcommand{\parallele}{\sslash} \newcommand{\para}{\sslash} \newcommand{\er}{\textsuperscript{er}\ } \newcommand{\eme}{\textsuperscript{ème}\ } \newcommand{\ere}{\textsuperscript{ère}\ } \newcommand{\snd}{\textsuperscript{nd}\ } \newcommand{\snde}{\textsuperscript{nde}\ } \newcommand{\iem}{\textsuperscript{ième}\ } \newcommand{\x}{\times} \newcommand{\ie}{\leqslant} \newcommand{\se}{\geqslant} \newcommand{\qqquad}{\quad\qquad} \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\D}{\mathbb D} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \newcommand{\F}{\mathbb F} \newcommand{\K}{\mathbb K} \newcommand{\U}{\mathbb U} %\newcommand{\Code}[1]{ {\verb+#1+} } \newcommand{\Code}[1]{{\ttfamily #1}} %\newcommand{\partent}{\mathsf{ent}} \newcommand{\E}{\mathsf{E}} %\newcommand{\alea}{\verb?alea?} \newcommand{\partent}{\text{\Code{ent}} } \newcommand{\alea}{\text{\Code{alea}} } \newcommand{\epsi}{\varepsilon} % epsilonn \newcommand{\f}{\othervarphi} % fonction phi \newcommand{\g}{\gamma} \newcommand{\al}{\alpha} \newcommand{\de}{\delta} \newcommand{\De}{\Delta} \newcommand{\Ga}{\Gamma} \newcommand{\La}{\Lambda} \newcommand{\la}{\lambda} \renewcommand{\o}{\otheromega} \newcommand{\si}{\sigma} \newcommand{\Ta}{\Theta} \newcommand{\teta}{\theta} \renewcommand{\O}{\Omega} \newcommand{\prive}{\setminus}%{\backslash} \newcommand{\union}{\cup} \newcommand{\inter}{\cap} \newcommand{\vide}{\varnothing} \newcommand{\card}{\mathop{\rm card}\nolimits} \newcommand{\paire}[2]{\{#1\, ;\, #2\}} \newcommand{\Paire}[2]{\left\{#1\, ;\, #2\right\}} \newcommand{\enstrois}[3]{\{#1\, ;\, #2\, ;\, #3\}} \newcommand{\Enstrois}[3]{\left\{#1\, ;\, #2\, ;\, #3\right\}} \newcommand{\ensquatre}[4]{\{#1\, ;\, #2\, ;\, #3\, ;\, #4\}} \newcommand{\Ensquatre}[4]{\left\{#1\, ;\, #2\, ;\, #3\, ;\, #4\right\}} \newcommand{\triplet}[3]{(#1\, ;\, #2\, ;\, #3)} \newcommand{\quadruplet}[4]{(#1\, ;\, #2\, ;\, #3\, ; #4)} \newcommand{\nuplet}[2]{(#1\, ;\,\ldots\, ;\, #2)} \newcommand{\Nuplet}[2]{\left(#1\, ;\,\ldots\, ;\, #2\right)} \newcommand{\ensemble}[2]{\{#1\, ;\,\ldots\, ;\, #2\}} \newcommand{\interieur}[1]{\ring{#1}} \newcommand{\ens}[1]{\left\{\,#1\,\right\}} \newcommand{\tq}{ \ \ \textrm{t.q} \ \ } \newcommand{\tqc}{ \textrm{t.q} } \newcommand{\Frac}[2]{\frac{\disp #1}{\disp #2}} \newcommand{\tvi}[2]{\vrule height #1 depth #2 width 0pt} \newcommand{\rond}{\circ} \newcommand{\ps}{\cdot} \newcommand{\ovra}[3]{\mkern #1mu\overrightarrow{\mkern -#1mu #2\mkern -#3mu}\mkern #3mu} \newcommand{\ovla}[3]{\mkern #1mu\overleftarrow{\mkern -#1mu #2\mkern -#3mu}\mkern #3mu} \newcommand{\delim}[3]{\raise #1\hbox{$\left #2\vbox to #3{}\right.$}} \renewcommand{\(}{\left( } \renewcommand{\)}{\right) } \newcommand{\oc}{\left[} \newcommand{\fc}{\right]} \newcommand{\norme}[1]{\| #1 \|} \newcommand{\normebis}[1]{\delim{2pt}{\|}{9pt}\! #1\delim{2pt}{\|}{9pt}} \newcommand{\normetriple}[1]{\left |\kern -.07em\left\| #1\right |\kern -.07em\right\|} \newcommand{\valabs}[1]{\delim{2pt}{|}{9pt}#1\delim{2pt}{|}{9pt}} \newcommand{\Abs}[1]{\left \lvert#1\right \rvert} \newcommand{\dist}[2]{\textrm{d}(#1\textrm{;\,} #2)} \newcommand{\limit}[2]{\displaystyle\lim_{#1} #2} \newcommand{\limitx}[3]{\displaystyle\lim_{#1\to #2} #3} \newcommand{\limitxinf}[3]{\displaystyle\lim_{#1\build{\to}_{<}^{} #2} #3} \newcommand{\limitxsup}[3]{\displaystyle\lim_{#1\build{\to}_{>}^{} #2} #3} \newcommand{\tend}[2]{\displaystyle\build\longrightarrow_{#1\rightarrow #2}^{}} \newcommand{\ds}{\displaystyle} \newcommand{\fonc}[4]{#1\ :\begin{array}{rll} #2 &\to \\ x& \mapsto  \end{array}} \newcommand{\Fonc}[5]{#1\ :\begin{array}{rll} #2 &\to \\ #4& \mapsto  \end{array}} \newcommand{\limd}[2][x]{\ds\lim_{{#1\to #2}\atop{#1>#2}} } \newcommand{\limcd}[1]{\ds\lim_{#1^+} } \newcommand{\limg}[2][x]{\ds\lim_{{#1\to #2}\atop{#1<#2}} } \newcommand{\limcg}[1]{\ds\lim_{#1^-} } \newcommand{\limc}[1]{\ds\lim_{#1} } \newcommand{\lin}{\ds\lim_{n\to +\infty}} \newcommand{\Lim}[2][x]{\displaystyle{\lim_{#1 \to #2}}} \newcommand{\Li}[2]{\left.\begin{array}{lcr} #1\\ #2 \end{array}\right\}} \newcommand{\somme}[3][i]{\sum\limits_{\substack{#1=#2}}^{#3}} \newcommand{\Tendvers}[2][h]{\underset{#1\rightarrow #2}{\longrightarrow}} \newcommand{\un}{{(u_n)}_{n\in\N}\ } % suite un {(t_{n})}_{n\in\N} \newcommand{\unstar}{{(u_n)}_{n\in\N^{\ast}}\ } % suite un \newcommand{\vn}{{(v_n)}_{n\in\N}\ } %suite vn \newcommand{\wn}{{(w_n)}_{n\in\N}\ } %suite wn \newcommand{\tn}{{(t_n)}_{n\in\N}\ } %suite tn \newcommand{\sn}{{(s_n)}_{n\in\N}\ } %suite tn \newcommand{\rn}{{(r_n)}_{n\in\N}\ } %suite tn \newcommand{\xn}{{(x_n)}_{n\in\N}\ } %suite tn \newcommand{\yn}{{(y_n)}_{n\in\N}\ } %suite tn \newcommand{\zn}{{(z_n)}_{n\in\N}\ } %suite tn \newcommand{\an}{{(a_n)}_{n\in\N}\ } %suite tn \newcommand{\bn}{{(b_n)}_{n\in\N}\ } %suite tn \newcommand{\cn}{{(c_n)}_{n\in\N}\ } %suite tn \newcommand{\dn}{{(d_n)}_{n\in\N}\ } %suite tn \newcommand{\en}{{(e_n)}_{n\in\N}\ } %suite tn \newcommand{\enstar}{{(e_n)}_{n\in\N^{\ast}}\ } % suite un % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Equivalent \newcommand{\equivalent}[1]{\build\sim_{#1}^{}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% o et O \renewcommand{\o}[2]{\build o_{#1\to #2}^{}} \renewcommand{\O}[2]{\build O_{#1\to #2}^{}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Displaystyle \newcommand{\disp}{\displaystyle} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signes d'equivalence et d'implication \newcommand{\equivaut}{\Longleftrightarrow} \newcommand{\equi}{\Leftrightarrow} \newcommand{\implique}{\Longrightarrow} \newcommand{\impli}{\Rightarrow} \newcommand{\ssi}{\textrm{ \ ssi \ }} \newcommand{\idest}{\quad \textrm{i.e} \quad} \newcommand{\cad}{\quad \textrm{c-à-d} \quad} % \newcommand{\ssic}{\textrm{ssi} } \newcommand{\idestc}{\textrm{i.e} } \newcommand{\cadc}{\textrm{c-à-d}} \newcommand{\maxi}{ \textrm{max}} \newcommand{\sgn}{\textrm{sgn}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signe associe \newcommand{\associe}{\longmapsto} \newcommand{\asso}{\mapsto} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Angles \renewcommand{\angle}[1]{\widehat{#1}} \newcommand{\anglevec}[2]{(\vec #1\, ,\,\vec #2)} \newcommand{\Anglevec}[2]{(\V{#1}\, ,\,\V{#2})} \newcommand{\anglecouple}[2]{\left( #1\, ,\, #2 \right) } %\newcommand{\anglevecteur0}[3][black]{(\widehat{\vec{#2}\, , \, \textcolor{#1}{\vec{#3}}})} %\newcommand{\anglevecteur}[4][black]{\anglevecteur0{#2}{ \textcolor{#1}{#3} }{#4} } \newcommand{\anglevecteur}[2]{(\widehat{\vec{#1}\, , \, \vec{#2}} ) } %\newcommand{\anglevecteurcouleur}[4]{(\textcolor{#1}{\vec{#3}}\, , \, \textcolor{#2}{\vec{#4}}) } \newcommand{\Anglevecteur}[2]{\(\widehat{\V{#1},\V{#2}}\)} \newcommand{\rad}{ \,\,\textrm{rad} } \newcommand{\mes}{\textrm{mes} } \newcommand{\°}{\degres} \newcommand{°}{\degres} \newcommand{\Mes}[1]{\mes\,\widehat{#1}} \newcommand{\mesvec}[2]{\textrm{mes}\(\vec{#1} \, , \, \vec{#2}\)} \newcommand{\mesvecteur}[2]{\textrm{mes}\anglevecteur{#1}{#2}} \newcommand{\mesVec}[2]{\textrm{mes}\(\V{#1} \, , \, \V{#2}\)} \newcommand{\mesarc}[1]{\textrm{mes}\(\widehat{#1}\)} \newcommand{\mesarco}[1]{\textrm{mes}\(\arcoriente{#1}\)} \newcommand{\ao}[2]{\left(#1\, , \, #2\right)} %\newcommand{\Mes}[1]{% % \ensuremath{% % \mathrm{mes} % \DecalV{\widehat{#1}} % }} %\DeclareTextSymbol{\degree}{T1}{6} %\DeclareTextSymbol{\degre}{OT1}{23} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Vecteurs %\newcommand{\vecteur}[1]{\ovra 0{#1}0} \newcommand{\prodscal}[2]{<#1,#2>} \newcommand{\prodvec}[2]{#1\wedge #2} \newcommand{\vectoriel}[2]{\prodvec{\vec #1}{\vec #2}} \newcommand{\Vectoriel}[2]{\prodvec{\vecteur{#1}}{\vecteur{#2}}} \newcommand{\prodmixte}[3]{\big[#1, #2, #3\big]} \newcommand{\mixte}[3]{\prodmixte{\vec #1}{\vec #2}{\vec #3}} \newcommand{\Mixte}[3]{\prodmixte{\vecteur{#1}}{\vecteur{#2}}{\vecteur{#3}}} \newcommand{\V}[1]{\ovra 0{#1}0} % \newcommand{\test}[2]{#1^2-#2^2} % %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Repères (O,i), (O,i,j), (O,u,v), (O,I,J) et quelconques \newcommand{\Oi}{(O\, ;\,\vec\imath\,)} \newcommand{\Oj}{(O\, ;\,\vec\jmath\,)} \newcommand{\Oij}{(O\, ;\,\vec\imath\, ;\vec\jmath\,)} \newcommand{\Aij}{(A\, ;\,\vec\imath\, ;\vec\jmath\,)} \newcommand{\Omegaij}{(\Omega\, ;\,\vec\imath\, ;\vec\jmath\,)} \newcommand{\Ai}{(A\, ;\,\vec\imath\,)} \newcommand{\Aj}{(A\, ;\,\vec\jmath\,)} \newcommand{\Ojk}{(O\, ;\,\vec\jmath\, ;\vec k\,)} \newcommand{\Oik}{(O\, ;\,\vec\imath\, ;\vec k\,)} \newcommand{\Ouv}{(O\, ;\,\vec u\, ;\vec v\,)} \renewcommand{\ij}{(\vec\imath\, ;\vec\jmath\,)} \newcommand{\ijk}{(\vec\imath\, ;\vec\jmath\, ;\vec k\,)} \newcommand{\Oijk}{\big(O\, ;\,\vec\imath\, ;\vec\jmath\, ;\vec k\,\big)} \newcommand{\oijk}{\big(o\, ;\,\vec\imath\, ;\vec\jmath\, ;\vec k\,\big)} \newcommand{\OIJ}{(O\,;\, I\,;\, J\,)} \newcommand{\repere}[3]{\big(#1\, ;\,\vecteur{#2} ;\vecteur{#3}\big)} \newcommand{\reperesp}[4]{\big(#1\, ;\,\vecteur{#2} ;\vecteur{#3} ;\vecteur{#4}\big)} % \newcommand{\reperepol}[2]{\big(#1\, ;\,\vecteur{#2}\big)} \newcommand{\reperesf}[3]{\big(#1\, ;\,#2 ; #3 \big)} % %Redéfinition de \longrightarrow %\newcommand\longrightarrow{\mathrel{\raise .02em\hbox{$\relbar$}}\joinrel\rightarrow} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Aire d'une surface \newcommand{\aire}[1]{% \ensuremath{\mathscr{A}_{#1}}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Volume d'un volume \newcommand{\volume}[1]{% \ensuremath{\mathscr{V}_{#1}}} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% un ; avec un peu d'espace autour \newcommand{\pv}{\ensuremath{\: ; \,}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intervalles \newcommand{\interoo}[2]{]#1\, ;\, #2[} \newcommand{\Interoo}[2]{\left]#1\, ;\, #2\right[} \newcommand{\interof}[2]{]#1\, ;\, #2]} \newcommand{\Interof}[2]{\left]#1\, ;\, #2\right]} \newcommand{\interfo}[2]{[#1\, ;\, #2[} \newcommand{\Interfo}[2]{\left[#1\, ;\, #2\right[} \newcommand{\interff}[2]{[#1\, ;\, #2]} \newcommand{\Interff}[2]{\left[#1\, ;\, #2\right]} % \newcommand{\of}[2]{\left] \,#1 \, ; \, #2 \,\right] } \newcommand{\fo}[2]{\left[ \,#1 \, ; \, #2 \,\right[ } \newcommand{\oo}[2]{\left] \,#1 \, ; \, #2 \,\right[ } \newcommand{\ff}[2]{\left[ \,#1 \, ; \, #2 \,\right] } % %\newcommand\interentiers #1#2{[\! [#1\, ;\, #2]\! ]} \newcommand{\interentiers}[2]{\llbracket #1\, ;\, #2\rrbracket} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% autres intervalles \newcommand{\Intff}[2]{\ensuremath{\left[#1\pv #2\right]}} \newcommand{\Intfo}[2]{\ensuremath{\left[#1\pv #2\right[}} \newcommand{\Intof}[2]{\ensuremath{\left]#1\pv #2\right]}} \newcommand{\Intoo}[2]{\ensuremath{\left]#1\pv #2\right[}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées %\newcommand{\coord}[2]{(#1\, ;\, #2)} \newcommand{\bigcoord}[2]{\big(#1\, ;\, #2\big)} \newcommand{\coord}[2]{\left(#1\, ;\, #2\right)} \newcommand{\Coord}[2]{\left(#1\, ;\, #2\right)} \newcommand{\coordesp}[3]{(#1\, ;\, #2\, ;\, #3)} \newcommand{\bigcoordesp}[3]{\big(#1\, ;\, #2\, ;\, #3\big)} \newcommand{\Coordesp}[3]{\left(#1\, ;\, #2\, ;\, #3\right)} \newcommand{\coordpol}[2]{\left[#1\, ;\, #2\right]} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées verticales dans le plan \newcommand{\coordp}[2]{% \begin{pmatrix} #1 \\ #2 \end{pmatrix}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Coordonnées verticales dans l'espace \newcommand{\coordpp}[3]{% \scalebox{.7}{% \begin{pmatrix} #1 \\ #2 \\ #3 \end{pmatrix}}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Congruences \newcommand{\congru}{\equiv} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Modulo 2pi ou autre \newcommand{\Mod}[1][2\pi]{\enspace{(#1)}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Quel que soit \newcommand{\qqsoit}{\forall\,} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Différentielles \renewcommand{\d}{\textrm d} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intégrale \newcommand{\integ}[4]{\int_{#1}^{#2} #3\,\d #4} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Intégration par parties \newcommand{\intpp}[4]{% $\left\{% \begin{matrix} #1 & #3 \\ \stackrel{}{#2} & \stackrel{}{#4} \\ \end{matrix} \right.$} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Somme majuscule \newcommand{\Sum}{\displaystyle{\sum}} % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Barycentres \newcommand{\bary}{\mathop{\rm Bar}\nolimits} \newcommand{\baryd}[4]{\(#1\, ;\, #2\)\ \textrm{et}\ \(#3\, ;\, #4 \)} \newcommand{\baryt}[6]{(#1\, ;\, #2),\ (#3\, ;\, #4)\ \textrm{et}\ (#5\, ;\, #6)} \newcommand{\baryq}[8]{(#1\, ;\, #2),\ (#3\, ;\, #4),\ (#5\, ;\, #6)\ \textrm{et}\ (#7\, ;\, #8)} \newcommand{\Baryd}[4]{\bary \left\lbrace \(#1\, ;\, #2 \)\, ;\, \(#3\, ;\, #4 \) \right\rbrace } \newcommand{\Baryt}[6]{\bary \left\lbrace \(#1\, ;\, #2\)\, ;\, \(#3\, ;\, #4 \)\, ;\, \(#5\, ;\, #6 \) \right\rbrace } \newcommand{\Baryn}[6]{\bary \left\lbrace \(#1\, ;\, #2\)\, ;\, \(#3\, ;\, #4 \)\, ;\,\ldots\, ;\, \(#5\, ;\, #6\) \right\rbrace } % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Signe inclusion \newcommand{\inclus}{\subset} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonctions \newcommand{\fonction}[5]{ \begin{eqnarray*} #1 & \!\!\!\!\! : & \!\!\!\!\! #2\longrightarrow #3\\ & & \!\!\!\!\! #4\longmapsto #5 \end{eqnarray*} } \newcommand{\fonctionligne}[5]{#1:#2\longrightarrow #3,\ #4\longmapsto #5} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Unités de longueur en rm \newcommand{\cm}{\mathop{\rm cm}\nolimits} \newcommand{\mm}{\mathop{\rm mm}\nolimits} \newcommand{\dm}{\mathop{\rm dm}\nolimits} \newcommand{\m}{\mathop{\rm m}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction logarithme intégral [Plt137] \newcommand{\li}{\mathop{\rm li}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction exponentielle \newcommand{\e}{\mathop{\rm e}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonction cotangente \newcommand{\cotan}{\mathop{\rm cotan}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fonctions hyperboliques \newcommand{\ch}{\mathop{\rm ch}\nolimits} \newcommand{\sh}{\mathop{\rm sh}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Parties entière, réelle, imaginaire, nombre i \newcommand{\ent}{\mathop{\rm E}\nolimits} \newcommand{\Int}{\mathop{\rm Int}\nolimits} \renewcommand{\Re}{\mathop{\rm Re}\nolimits} \renewcommand{\Im}{\mathop{\rm Im}\nolimits} \renewcommand{\i}{\textrm{i}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Comatrice \newcommand{\com}{\mathop{\rm com}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Trace \newcommand{\tr}{\mathop{\rm tr}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Transposée \newcommand{\transposee}[1]{{\vphantom{#1}}^t\negmedspace #1} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Noyau \newcommand{\Ker}{\mathop{\rm Ker}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% PGCD, PPCM \newcommand{\PGCD}{\mathop{\rm PGCD}\nolimits} \newcommand{\PPCM}{\mathop{\rm PPCM}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Matrices \newcommand{\Mn}{\mathcal M_n} \newcommand{\matrice}[4]{ \left( \begin{array}{cc} #1 & #2 \\ #3 & #4 \end{array} \right)} \newcommand{\vect}[2]{ \left(\negmedspace \begin{array}{c} #1\\ #2 \end{array}\negmedspace \right)} \newcommand{\Matrice}[9]{ \left( \begin{array}{ccc} #1 & #2 & #3\\ #4 & #5 & #6\\ #7 & #8 & #9 \end{array} \right)} \newcommand{\Vect}[3]{ \left(\negmedspace \begin{array}{c} #1\\ #2\\ #3 \end{array}\negmedspace \right)} \newcommand{\Ideux}{\matrice{1}{0}{0}{1}} \newcommand{\Itrois}{\Matrice{1}{0}{0}{0}{1}{0}{0}{0}{1}} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Determinants \newcommand{\determinant}[4]{ \left| \begin{array}{cc} #1 & #3 \\ #2 & #4 \end{array} \right|} \newcommand{\Determinant}[9]{ \left| \begin{array}{ccc} #1 & #2 & #3\\ #4 & #5 & #6\\ #7 & #8 & #9 \end{array} \right|} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Systemes \newcommand{\sysu}[1]{ \left\lbrace \begin{array}{l} #1\\ \end{array} \right.} \newcommand{\sys}[2]{ \left\lbrace \begin{array}{l} \negthickspace\negthickspace #1\\ \negthickspace\negthickspace #2\\ \end{array} \right.\negthickspace\negthickspace} \newcommand{\sysd}[2]{ %\left\lbrace \left\{ \begin{array}{l} #1\\ #2 \end{array} \right.} %%%%%%%%%%%%%%%%%%%%%%%% %\left\{\begin{array}{l c l} %v_{0} &=& 1\\ %v_{n + 1}&=& \dfrac{9}{6 - v_{n}} %\end{array}\right. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\syst}[3]{ \left\lbrace \begin{array}{l} #1\\ #2\\ #3\\ \end{array} \right.} \newcommand{\sysq}[4]{ \left\lbrace \begin{array}{l} #1\\ #2\\ #3\\ #4\\ \end{array} \right.} \newcommand{\sysc}[5]{ \left\lbrace \begin{array}{l} #1\\ #2\\ #3\\ #4\\ #5\\ \end{array} \right.} \newcommand{\sisi}[4]{ \left\lbrace \begin{array}{rm{0.2cm}l} #1 & & \text{#2}\\ #3 & & \text{#4} \end{array} \right.} % %\newcommand{\accod}[4]{\begin{cases} #1 & #2 \\ #3 & #4 \end{cases} } % \newcommand{\accot}[6]{\begin{cases} #1 & #2 \\ #3 & #4 \\ #5 & #6 \end{cases} } %% %\newcommand{\accod}[2]{ \left\{ % \begin{split} % #1 \\ % #2 % \end{split} % \right. } % \newcommand{\accott}[3]{ \begin{equation} \left\{ \begin{split} #1 \\ #2 \\ #3 \end{split} \right. \end{equation} } \newcommand{\Syst}[2]{\left\{\begin{array}{ccccc} #1\\ #2 \end{array}\right.} % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Covariance \newcommand{\cov}{\mathop{\rm cov}\nolimits} % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Symboles entre droites %\newcommand{\paral}{\sslash} \newcommand{\paral}{\mathop{/\!\! /}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% jours heures minutes secondes \newcommand{\jour}{\ \textrm{j} \ } \newcommand{\heure}{\ \textrm{h} \ } \newcommand{\minute}{\ \textrm{min} \ } \newcommand{\seconde}{\ \textrm{s} \ } \newcommand{\algobox}{\texttt{AlgoBox}} \newcommand{\xcas}{\texttt{Xcas}} \newcommand{\excel}{\texttt{Excel}\ } \newcommand{\calc}{\texttt{Calc}} \newcommand{\geogebra}{\texttt{GeoGebra}} \newcommand{\python}{\texttt{Python}\ } \newcommand{\ou}{ \quad \text{ ou } \quad } \newcommand{\et}{ \quad \text{ et } \quad } \newcommand{\btr}{\ensuremath{\blacktriangleright\ }} \newcommand{\wtr}{\ensuremath{\triangleright\ }} \newcommand{\bp}{\ensuremath{\bullet\ }} %%%%%%%%%%%%%%%%%%%%% B(n;p) - Loi binomiale %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\bnp}[2][n]{\ensuremath{\mathscr B\(#1 \pv #2 \)}} $

CH01 - Divisibilité et congruences
Éléments historiques
 
CH08 - Matrices et opérations
Corrigé du DS MO3
Corrigé du DS MO2
Corrigé du DS MO1
Corrections des exercices
Exercices supplémentaires corrigés :

Pour s'entraîner en ligne :
Des vidéos sur le chapitre :
Éléments historiques
 
CH04 - Nombres complexes : point de vue algébrique
Corrigé du DS (30/09)
Corrections des exercices
Quelques vidéos sur le chapitre :
Éléments historiques
Exercices supplémentaires corrigés :

 
Du lycée aux CPGE scientifiques
Lorsqu’on discute avec des lycéens se destinant aux CPGE scientifiques, deux questions reviennent fréquemment :
  • Comment un lycéen peut-il se préparer efficacement aux CPGE, ou, plus largement, à des études supérieures scientifiques ?
  • Quelles sont les mathématiques accessibles à un lycéen intéressé par la discipline et désirant un peu dépasser le programme de terminale ?
Un groupe de professeurs des lycées Louis-Le-Grand et Henri-IV ont élaboré un document pour répondre à ces deux demandes.
Ce document, qui peut être travaillé dès le début de l’année de terminale, voire avant pour certaines parties, n’a pas vocation à se substituer aux cours du lycée, mais plutôt à les compléter. Il peut aussi donner des points de départ pour le « grand oral » du baccalauréat.
Mathématiques : du lycée aux CPGE scientifiques
 
Baccalauréat
Deux simulateurs de moyenne au bac intéressants :   sujetdebac.fr   -   letudiant.fr
Le Grand oral : En voie générale et technologique, vous passez un Grand oral à la fin de votre année de terminale. Cette épreuve fait partie des 5 épreuves finales du baccalauréat (60% de la note finale) et compte avec un coefficient 10 en voie générale ou 14 en voie technologique. Cette épreuve dure 20 minutes et est précédée de 20 minutes de préparation.
Plus de détails
Nouveau bac : tout est très bien expliqué dans cette vidéo (coefficients, contrôle continu, épreuves finales, 1ère et Tale).
 
Prélude
Présentation & fonctionnement des cours
Alain Connes, membre de l'Académie des sciences, est Professeur au Collège de France, à l'I.H.E.S. et à l'Université OSU, Columbus aux États-Unis. Alain Connes a notamment reçu la Médaille Fields en 1982, le Prix Crafoord en 2001 et la Médaille d'or du C.N.R.S. en 2004.
Pour vous aider dans votre projet d'orientation, pensez à consulter le site de l'ONISEP qui contient de nombreuses informations utiles.