Commit 67515d4c authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 201c1209
Pipeline #13542 canceled with stage
...@@ -92,10 +92,23 @@ $`\overrightarrow{grad}\,f=\left( ...@@ -92,10 +92,23 @@ $`\overrightarrow{grad}\,f=\left(
      donc :       donc :
$`\overrightarrow{grad}\big(div\,\overrightarrow{U}\big)`$ $`\overrightarrow{grad}\big(\color{blue}{div\,\overrightarrow{U}}\big)`$
$`\quad = \left( $`\quad = \left(
\begin{array}{l} \begin{array}{l}
\dfrac{\partial}{\partial x}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}} \right)\\ \dfrac{\partial}{\partial x}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}} \right)\\
\dfrac{\partial}{\partial y}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}} \right)\\ \dfrac{\partial}{\partial y}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}} \right)\\
\dfrac{\partial}{\partial z}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}} \right) \dfrac{\partial}{\partial z}\left( \color{blue}{\dfrac{\partial U_x}{\partial x}+\dfrac{\partial U_y}{\partial y}+\dfrac{\partial U_z}{\partial z}} \right)
\end{array}\right)`$ \end{array}\right)`$
      et nous obtenons :
$`\overrightarrow{grad}\big(div\,\overrightarrow{U}\big)`$
$`\quad = \left(
\begin{array}{l}
\dfrac{\partial^2 U_x}{\partial x^2}+\partial^2 U_y}{\partial x \partial y}+\partial^2 U_z}{\partial x \partial z}\\
\dfrac{\partial^2 U_x}{\partial y \partial x}+\partial^2 U_y}{\partial y^2}+\partial^2 U_z}{\partial y \partial z}\\
\dfrac{\partial^2 U_x}{\partial z \partial x}+\partial^2 U_y}{\partial z \partial y}+\partial^2 U_z}{\partial z^2}
\end{array}\right)`$
\end{array}\right)`$
\ No newline at end of file
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