Commit 05f857ff authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 53c2a43b
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...@@ -117,22 +117,18 @@ visible: false ...@@ -117,22 +117,18 @@ visible: false
\;\left(\dfrac{\partial^2 U_z}{\partial x^2}+\dfrac{\partial^2 U_z}{\partial y^2}+\dfrac{\partial^2 U_z}{\partial z^2}\right)-\dfrac{1}{\mathscr{v}^2}\dfrac{\partial^2 U_z}{\partial t^2}=0 \;\left(\dfrac{\partial^2 U_z}{\partial x^2}+\dfrac{\partial^2 U_z}{\partial y^2}+\dfrac{\partial^2 U_z}{\partial z^2}\right)-\dfrac{1}{\mathscr{v}^2}\dfrac{\partial^2 U_z}{\partial t^2}=0
\end{array}\right.`$* \end{array}\right.`$*
<br> <br>
**Chacune des composantes du champ vérifie l'équation d'onde scalaire**. *Chacune des composantes du champ vérifie l'équation d'onde scalaire*.
* L'expression du laplacien vectoriel **$`\overrightarrow{\Delta}\,\overrightarrow{U}`$** * L'expression du laplacien vectoriel **$`\overrightarrow{\Delta}\,\overrightarrow{U}`$**
d'un vecteur $`\overrightarrow{U}`$ **en coordonnées cartésiennes** est : d'un vecteur $`\overrightarrow{U}`$ **en coordonnées cartésiennes** est :
<br> <br>
**$`\overrightarrow{\Delta}= **$`\overrightarrow{\Delta}=\left(\begin{array}{l}
\left(
\begin{array}{l}
\dfrac{\partial^2 U_x}{\partial x^2} + \dfrac{\partial^2 U_x}{\partial y^2} + \dfrac{\partial^2 U_x}{\partial z^2}\\ \dfrac{\partial^2 U_x}{\partial x^2} + \dfrac{\partial^2 U_x}{\partial y^2} + \dfrac{\partial^2 U_x}{\partial z^2}\\
\dfrac{\partial^2 U_y}{\partial x^2} + \dfrac{\partial^2 U_y}{\partial y^2} + \dfrac{\partial^2 U_y}{\partial z^2}\\ \dfrac{\partial^2 U_y}{\partial x^2} + \dfrac{\partial^2 U_y}{\partial y^2} + \dfrac{\partial^2 U_y}{\partial z^2}\\
\dfrac{\partial^2 U_z}{\partial x^2} + \dfrac{\partial^2 U_z}{\partial y^2} + \dfrac{\partial^2 U_z}{\partial z^2 \dfrac{\partial^2 U_z}{\partial x^2} + \dfrac{\partial^2 U_z}{\partial y^2} + \dfrac{\partial^2 U_z}{\partial z^2
\end{array} \end{array}\right)`$**
\right)`$**
**$`\overrightarrow{\Delta}= **$`\overrightarrow{\Delta}=\begin{pmatrix}
\begin{pmatrix}
\dfrac{\partial^2 U_x}{\partial x^2} + \dfrac{\partial^2 U_x}{\partial y^2} + \dfrac{\partial^2 U_x}{\partial z^2}\\ \dfrac{\partial^2 U_x}{\partial x^2} + \dfrac{\partial^2 U_x}{\partial y^2} + \dfrac{\partial^2 U_x}{\partial z^2}\\
\dfrac{\partial^2 U_y}{\partial x^2} + \dfrac{\partial^2 U_y}{\partial y^2} + \dfrac{\partial^2 U_y}{\partial z^2}\\ \dfrac{\partial^2 U_y}{\partial x^2} + \dfrac{\partial^2 U_y}{\partial y^2} + \dfrac{\partial^2 U_y}{\partial z^2}\\
\dfrac{\partial^2 U_z}{\partial x^2} + \dfrac{\partial^2 U_z}{\partial y^2} + \dfrac{\partial^2 U_z}{\partial z^2 \dfrac{\partial^2 U_z}{\partial x^2} + \dfrac{\partial^2 U_z}{\partial y^2} + \dfrac{\partial^2 U_z}{\partial z^2
......
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