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diff --git a/macros/latex/contrib/tkz/tkz-fct/doc/latex/TKZdoc-fct-VDW.tex b/macros/latex/contrib/tkz/tkz-fct/doc/latex/TKZdoc-fct-VDW.tex deleted file mode 100644 index 0f5a4a45ff..0000000000 --- a/macros/latex/contrib/tkz/tkz-fct/doc/latex/TKZdoc-fct-VDW.tex +++ /dev/null @@ -1,149 +0,0 @@ - -\subsection{Courbes de \tkzname{Van der Waals}} - -\bigskip -Soient $v$ le volume d'une masse fluide et $p$ sa pression. -$b$ et $k$ sont deux nombres réels strictement positifs. On souhaite étudier une formule exprimant la dépendance de ces variables proposée par Van~der~Waals. -\[ - p(v)= \frac{-3}{v^2} + \dfrac{3k}{v-b} -\] - -définie sur l'intervalle $I=\big]b~;~+\infty\big]$ - -\subsubsection{Tableau de variations} -\begin{center} - - \begin{tkzexample}[] - \begin{tikzpicture} - \tkzTab% - { $v$ /1,% - $g'(v)$ /1,% - $g(v)$ /3% - }% - { $b$ ,% - $3b$ ,% - $+\infty$% - }% - {0,$+$,$0$,$-$,t} - {-/ $0$ /,% - +/$\dfrac{8}{27b}$ /,% - -/ $0$ /}% - \end{tikzpicture} -\end{tkzexample} -\end{center} - - - -\newpage - -\subsubsection{ Première courbe avec $ b=1$} - Quelques courbes pour $r\leq\ v \leq\ 6$ - -\medskip -\begin{center} - \begin{tkzexample}[] - \begin{tikzpicture}[xscale=2,yscale=2.5] - \tkzInit[xmin=0,xmax=6,ymax=0.5,ystep=0.1] - \tkzDrawX[label=$v$] - \tkzDrawY[label=$g(v)$] - \tkzGrid(0,0)(6,0.5) - \tkzFct[color = red,domain =1:6]{(2*(x-1)*(x-1))/(x*x*x)} - \tkzDrawTangentLine[color=blue,draw](3) - \tkzDefPointByFct(1) - \tkzText[draw, fill = brown!30](4,0.1){$g(v)=2\dfrac{(v-1)^2}{v^3}$} - \end{tikzpicture} - \end{tkzexample} -\end{center} - - -\newpage -\subsubsection{ Deuxième courbe $b=1/3$ } - - -\medskip -\begin{center} - \begin{tkzexample}[] - \begin{tikzpicture}[scale=1.2] - \tkzInit[xmin=0,xmax=2,xstep=0.2,ymax=1,ystep=0.1] - \tkzAxeXY - \tkzGrid(0,0)(2,1) - \tkzFct[color = red,domain =1/3:2]{(2*(\x-1./3)*(\x-1./3))/(\x*\x*\x)} - \tkzDrawTangentLine[draw,color=blue,kr=.5,kl=.5](1) - \tkzDefPointByFct(1) - \tkzText[draw,fill = brown!30](1.2,0.3)% - {$g(v)=2\dfrac{\left(v-\dfrac{1}{3}\right)^2}{v^3}$} - \end{tikzpicture} - \end{tkzexample} -\end{center} - - -\newpage -\subsubsection{ Troisième courbe $ b=32/27$ } - - -\medskip -\begin{center} - \begin{tkzexample}[] - \begin{tikzpicture}[scale=1.2] - \tkzInit[xmin=0,xmax=10,ymax=.35,ystep=0.05]; - \tkzAxeXY - \tkzGrid(0,0)(10,.35) - \tkzFct[color = red, - domain =1.185:10]{(2*(\x-32./27)*(\x-32./27))/(\x*\x*\x)} - \tkzDrawTangentLine[draw,color=blue,kr=2,kl=2](3.555) - \tkzText[draw,fill = brown!30](5,0.3)% - {$g(v)=2\dfrac{\left(v-\dfrac{32}{27}\right)^2}{v^3}$} - \end{tikzpicture} - \end{tkzexample} -\end{center} - - \newpage -\subsection{Valeurs critiques} -\subsubsection{Courbes de \tkzname{Van der Walls} } -%<–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––> - - -\begin{tkzexample}[] -\begin{tikzpicture}[scale=4] - \tkzInit[xmax=3,ymax=2]; - \tkzAxeXY - \tkzGrid(0,0)(3,2) - \tkzFct[color = red,domain =1/3:3]{0.125*(3*\x-1)+0.375*(3*\x-1)/(\x*\x)} - \tkzDefPointByFct[draw](2) - \tkzDefPointByFct[draw](3) - \tkzDrawTangentLine[draw,color=blue](1) - \tkzFct[color = green,domain =1/3:3]{0.125*(3*x-1)} - \tkzSetUpPoint[size=8,fill=orange] - \tkzDefPointByFct[draw](3) - \tkzDefPointByFct[draw](1/3) - \tkzDefPoint(1,1){f} - \tkzDrawPoint(f) - \tkzText[draw,fill = white,text=red](1,1.5)% -{$f(x)=\dfrac{1}{8}(3x-1)+\dfrac{3}{8}\left(\dfrac{3x-1}{x^2}\right)$} -\tkzText[draw,fill = white,text=green](2,0.4){$g(x) = \dfrac{3x-1}{8}$} -\end{tikzpicture} -\end{tkzexample} - -\newpage -\subsubsection{Courbes de \tkzname{Van der Walls} (suite)} - - -\begin{tkzexample}[] -\begin{tikzpicture}[xscale=4,yscale=1.5] - \tkzInit[xmin=0,xmax=3,ymax=3,ymin=-4] - \tkzGrid(0,-4)(3,3) - \tkzAxeXY - \tkzClip - \tkzVLine[color=red,style=dashed]{1/3} - \tkzFct[color=red,domain = 0.35:3]{-3/(x*x) +4/(3*x-1)} - \tkzFct[color=blue,domain = 0.35:3]{-3/(x*x) +27/(4*(3*x-1))} - \tkzFct[color=orange,domain = 0.35:3]{-3/(x*x) +8/(3*x-1)} - \tkzFct[color=green,domain = 0.35:3]{-3/(x*x) +7/(3*x-1)} - \tkzText[draw,fill = white,text=brown](2,-2)% - {$f(x)=-\dfrac{3}{x^2}+\dfrac{8\alpha}{3x-1}$ \hspace{.5cm}% - avec $\alpha \in% - \left\{\dfrac{1}{2}~;~\dfrac{27}{32}~;~\dfrac{7}{8}~;~1\right\}$} -\end{tikzpicture} -\end{tkzexample} - - \endinput
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