Commit 792ae479 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 09960b32
Pipeline #13305 canceled with stage
...@@ -446,11 +446,11 @@ $`\color{brown}{\mathbf{ ...@@ -446,11 +446,11 @@ $`\color{brown}{\mathbf{
##### Expression du gradient en coordonnées cartésiennes ##### Expression du gradient en coordonnées cartésiennes
$`\left.\begin{align} $`\left.\begin{array}{l}
dl_x=dx \Longrightarrow \dfrac{\partial x}{\partial l_x}=1\\ dl_x=dx \Longrightarrow \dfrac{\partial x}{\partial l_x}=1\\
dl_y=dy \Longrightarrow \dfrac{\partial y}{\partial l_y}=1\\ dl_y=dy \Longrightarrow \dfrac{\partial y}{\partial l_y}=1\\
dl_z=dz \Longrightarrow \dfrac{\partial z}{\partial l_z}=1\\ dl_z=dz \Longrightarrow \dfrac{\partial z}{\partial l_z}=1\\
\end{align}\right\}`$ \end{array}\right\}`$
$`\Longrightarrow\color{brown}{\mathbf{ $`\Longrightarrow\color{brown}{\mathbf{
\overrightarrow{grad}\,\phi= \overrightarrow{grad}\,\phi=
\dfrac{\partial \phi}{\partial x}\,\overrightarrow{e_x} \dfrac{\partial \phi}{\partial x}\,\overrightarrow{e_x}
...@@ -461,11 +461,11 @@ $`\Longrightarrow\color{brown}{\mathbf{ ...@@ -461,11 +461,11 @@ $`\Longrightarrow\color{brown}{\mathbf{
##### Expression du gradient en coordonnées cylindriques ##### Expression du gradient en coordonnées cylindriques
$`\left.\begin{align} $`\left.\begin{array}{l}
dl_{\rho}=d\rho\Longrightarrow \dfrac{\partial \rho}{\partial l_{\rho}}=1\\ dl_{\rho}=d\rho\Longrightarrow \dfrac{\partial \rho}{\partial l_{\rho}}=1\\
dl_{\varphi}=\rho\,d{\varphi} \Longrightarrow \dfrac{\partial \varphi}{\partial l_{\varphi}}=\dfrac{1}{\rho}\\ dl_{\varphi}=\rho\,d{\varphi} \Longrightarrow \dfrac{\partial \varphi}{\partial l_{\varphi}}=\dfrac{1}{\rho}\\
dl_z=dz \Longrightarrow \dfrac{\partial z}{\partial l_z}=1\\ dl_z=dz \Longrightarrow \dfrac{\partial z}{\partial l_z}=1\\
\end{align}\right\}`$ \end{array}\right\}`$
$`\Longrightarrow\color{brown}{\mathbf{ $`\Longrightarrow\color{brown}{\mathbf{
\overrightarrow{grad}\,\phi= \overrightarrow{grad}\,\phi=
\dfrac{\partial \phi}{\partial \rho}\,\overrightarrow{e_{\rho}} \dfrac{\partial \phi}{\partial \rho}\,\overrightarrow{e_{\rho}}
...@@ -475,11 +475,11 @@ $`\Longrightarrow\color{brown}{\mathbf{ ...@@ -475,11 +475,11 @@ $`\Longrightarrow\color{brown}{\mathbf{
##### Expression du gradient en coordonnées sphériques ##### Expression du gradient en coordonnées sphériques
$`\left.\begin{align} $`\left.\begin{array}{l}
dl_r=dr\Longrightarrow \dfrac{\partial r}{\partial l_r}=1\\ dl_r=dr\Longrightarrow \dfrac{\partial r}{\partial l_r}=1\\
dl_{\theta}=r\,d{\theta} \Longrightarrow \dfrac{\partial r}{\partial l_r}=\dfrac{1}{r}\\ dl_{\theta}=r\,d{\theta} \Longrightarrow \dfrac{\partial r}{\partial l_r}=\dfrac{1}{r}\\
dl_{\varphi}=r\,\sin\theta\,d\varphi \Longrightarrow \dfrac{\partial l_{\varphi}}{\partial l_{\varphi}}=\dfrac{1}{r\,\sin\theta}\\ dl_{\varphi}=r\,\sin\theta\,d\varphi \Longrightarrow \dfrac{\partial \varphi}{\partial l_{\varphi}}=\dfrac{1}{r\,\sin\theta}\\
\end{align}\right\}`$ \end{array}\right\}`$
$`\Longrightarrow\color{brown}{\mathbf{ $`\Longrightarrow\color{brown}{\mathbf{
\overrightarrow{grad}\,\phi= \overrightarrow{grad}\,\phi=
\dfrac{\partial \phi}{\partial r}\,\overrightarrow{e_r} \dfrac{\partial \phi}{\partial r}\,\overrightarrow{e_r}
......
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