diff --git a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md index 1112d150c..53d8e60bc 100644 --- a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md +++ b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md @@ -226,15 +226,23 @@ FR : en coordonnées cartésiennes orthonormées :
EN : in orthonormal Cartesian coordinate :
$`\Delta = \dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}+\dfrac{\partial^2}{\partial z^2}`$ -$`\Delta = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`$
-$`\Delta = \overrightarrow{grad}\:div\,\overrightarrow{U} - \overrightarrow{rot}\:\overrightarrow{rot}\,\overrightarrow{U}`$
+$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`$
+$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\:div\,\overrightarrow{U} - \overrightarrow{rot}\:\overrightarrow{rot}\,\overrightarrow{U}`$
ES : operador laplaciana vectorial, laplaciana vectorial, laplaciana de un campo vectorial
FR : opérateur laplacien, laplacien, d'un champ scalaire ou d'un champ vecoriel
-EN : laplacian operator, vectorial laplacian, laplacian of a vector field -in orthonormal Cartesian coordinate : +EN : laplacian operator, vectorial laplacian, laplacian of a vector field
+in orthonormal Cartesian coordinate :
$`\Delta\;\overrightarrow{U} = \overrightarrow{e_x}\left(\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2}\right) +\overrightarrow{e_y}\left(\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2}\right) -+\overrightarrow{e_z}\left(\dfrac{\partial^2\;U_z}{\partial x^2}+\dfrac{\partial^2\;U_z}{\partial y^2}+\dfrac{\partial^2\;U_z}{\partial z^2}\right)`$ ++\overrightarrow{e_z}\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)`$
+$`\Delta\;\overrightarrow{U} = \left \{ + \begin{array}{r c 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_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} + \end{array} + \right. + ES : escalar = número real o complexo + unidad de medida?
FR : scalaire = nombre réel ou complexe + unité de mesure