Update cheatsheet.fr.md

12.temporary_ins/32.sets-systems/30.n3/20.systems/20.overview/cheatsheet.fr.md

@@ -74,31 +74,7 @@ RÉSUMÉ<br>
   <br>
 
 
-  <br>
-  $`\displaystyle\begin{align}
-   \Large{\left.\dfrac{dN}{dt}\right\lvert_{\,\bigt} = r\,N(t)}&\quad \Longrightarrow\quad\left.\dfrac{dN}{N}\right\lvert_{\,\bigt}=r\,dt\\
-   \\
-  &\Longrightarrow\quad\int_{N(t_1)}^{N(t_2)}\dfrac{dN}{N}=\int_{t_1}^{t_2} r\,dt\\
-   \\
-   &\Longrightarrow\quad\big[\,ln\,|N|\,\big]_{N(t_1)}^{N(t_2)}= r \,\big[\,t\,\big]_{t_1}^{t_2}\\
-   \\
-   &\Longrightarrow\quad\underbrace{ln\,|N(t_2)|-\,ln\,|N(t_1)|}_{
-   N>0 \;\Longrightarrow\;|N|\,=\,N} = r\,(t_2 - t_1)\\
-   \\
-   &\Longrightarrow\quad ln\,N(t_2) = ln\,N(t_1) + r\,(t_2 - t_1)\\
-   \\
-   &\Longrightarrow\quad \underbrace{exp\big[ln\,N(t_2)\big]}_{exp(ln\,x)\;=\;x}
-   =\underbrace{exp\big[ln\,N(t_1) + r\,(t_2 - t_1)\big]}_{exp (a+b)\;=\;exp\,a\times exp\,b}\\
-   \\
-   &\Longrightarrow\quad N(t_2)=N(t_1)\,exp\,\big[r\,(t_2 - t_1)\big]\\
-   \\
-   &\Longrightarrow\quad \Large{N(t_2)=N(t_1)\;e^{\,r\,(t_2-t_1)}}
-   \end{align}`$
-   
-
-  <br>
-
-   $`\Large{\left.\dfrac{dN}{dt}\right\lvert_{\,\bigt} = r\,N(t)} \quad `$
+   $`\color{brown}{\Large{\left.\dfrac{dN}{dt}\right\lvert_{\,\bigt} = r\,N(t)}}`$
 
   $`\displaystyle\begin{align}
    \;\;&\Longrightarrow\quad\left.\dfrac{dN}{N}\right\lvert_{\,\bigt}=r\,dt\\
@@ -107,17 +83,17 @@ RÉSUMÉ<br>
    \\
    &\Longrightarrow\;\big[\,ln\,|N|\,\big]_{N(t_1)}^{N(t_2)}= r \,\big[\,t\,\big]_{t_1}^{t_2}\\
    \\
-   &\Longrightarrow\;\underbrace{ln\,|N(t_2)|-\,ln\,|N(t_1)|}_{
-   N>0 \;\Longrightarrow\;|N|\,=\,N} = r\,(t_2 - t_1)\\
+   &\Longrightarrow\;\underbrace{ln\,|N(t_2)|-\,ln\,|N(t_1)|}_{\color{blue}{
+   N>0 \;\Longrightarrow\;|N|\,=\,N}} = r\,(t_2 - t_1)\\
    \\
    &\Longrightarrow\; ln\,N(t_2) = ln\,N(t_1) + r\,(t_2 - t_1)\\
    \\
-   &\Longrightarrow\; \underbrace{exp\big[ln\,N(t_2)\big]}_{exp(ln\,x)\;=\;x}
-   =\underbrace{exp\big[ln\,N(t_1) + r\,(t_2 - t_1)\big]}_{exp (a+b)\;=\;exp\,a\;\times\; exp\,b}\\
+   &\Longrightarrow\; \underbrace{exp\big[ln\,N(t_2)\big]}_{\color{blue}{exp(ln\,x)\;=\;x}}
+   =\underbrace{exp\big[ln\,N(t_1) + r\,(t_2 - t_1)\big]}_{\color{blue}{exp (a+b)\;=\;exp\,a\;\times\; exp\,b}}\\
    \\
    &\Longrightarrow\; N(t_2)=N(t_1)\,exp\,\big[r\,(t_2 - t_1)\big]\\
    \\
-   &\Longrightarrow\; \Large{N(t_2)=N(t_1)\;e^{\,r\,(t_2-t_1)}}
+   &\color{brown}{\Longrightarrow\; \Large{N(t_2)=N(t_1)\;e^{\,r\,(t_2-t_1)}}}
    \end{align}`$