$ \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\| 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\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\(#1 \pv #2 \)}} $

CH03 - Dérivation locale
Questions flash & corrections des exercices
Figure dynamique illustrant l'exemple 2 du cours :

Des vidéos sur quelques compétences du chapitre.
Éléments historiques
 
CH02 - Suites numériques
Questions flash & corrections des exercices
Exercices supplémentaires corrigés :

Des vidéos sur les compétences du chapitre :
Les démonstrations des formules du cours

Sens de variation de la suite $(q^n)$ selon les valeurs du réel $q$.
Vous pouvez contrôler $q$ à l'aide du curseur.

Éléments historiques
 
CH01 - Second degré
Corrigé du DS
Corrigé de l'IE
Questions flash & corrections des exercices
Exercices supplémentaires corrigés :

Des vidéos revenant sur des compétences du chapitre :
Éléments historiques
 
Baccalauréat
Nouveau bac : tout est très bien expliqué dans cette vidéo (coefficients, contrôle continu, épreuves finales, 1ère et Tale).
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
 
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.