From b198b2fef13c5b914810587426d06ff8179201b0 Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Mon, 11 Nov 2019 19:02:33 +0100
Subject: [PATCH] Update textbook.en.md

---
 .../textbook.en.md                             | 18 +++++++++++++-----
 1 file changed, 13 insertions(+), 5 deletions(-)

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 :  <br>
 EN : in orthonormal Cartesian coordinate :  <br>
 $`\Delta = \dfrac{\partial^2}{\partial x^2}+\dfrac{\partial^2}{\partial y^2}+\dfrac{\partial^2}{\partial z^2}`$
 
-$`\Delta = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`$   <br>
-$`\Delta = \overrightarrow{grad}\:div\,\overrightarrow{U} - \overrightarrow{rot}\:\overrightarrow{rot}\,\overrightarrow{U}`$   <br>
+$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\left( div\,\overrightarrow{U}\right) - \overrightarrow{rot}\left(\overrightarrow{rot}\,\overrightarrow{U}\right)`$   <br>
+$`\Delta\;\overrightarrow{U} = \overrightarrow{grad}\:div\,\overrightarrow{U} - \overrightarrow{rot}\:\overrightarrow{rot}\,\overrightarrow{U}`$   <br>
 ES : operador laplaciana vectorial, laplaciana vectorial, laplaciana de un campo vectorial   <br>
 FR : opérateur laplacien, laplacien, d'un champ scalaire ou d'un champ vecoriel   <br>
-EN : laplacian operator, vectorial laplacian, laplacian of a vector field
-in orthonormal Cartesian coordinate :
+EN : laplacian operator, vectorial laplacian, laplacian of a vector field <br>
+in orthonormal Cartesian coordinate : <br>
 $`\Delta\;\overrightarrow{U} = \overrightarrow{e_x}\left(\dfrac{\partial^2\;U_x}{\partial x^2}+\dfrac{\partial^2\;U_x}{\partial y^2}+\dfrac{\partial^2\;U_x}{\partial z^2}\right)
 +\overrightarrow{e_y}\left(\dfrac{\partial^2\;U_y}{\partial x^2}+\dfrac{\partial^2\;U_y}{\partial y^2}+\dfrac{\partial^2\;U_y}{\partial z^2}\right)
-+\overrightarrow{e_z}\left(\dfrac{\partial^2\;U_z}{\partial x^2}+\dfrac{\partial^2\;U_z}{\partial y^2}+\dfrac{\partial^2\;U_z}{\partial z^2}\right)`$
++\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)`$ <br>
+$`\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?   <br>
 FR : scalaire = nombre réel ou complexe + unité de mesure   <br>