From 729b14eef43fd9d578f03bb6835ab06945590cba Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Mon, 11 Nov 2019 18:21:27 +0100
Subject: [PATCH] Update textbook.en.md

---
 .../textbook.en.md                            | 19 +++++++++++++++++--
 1 file changed, 17 insertions(+), 2 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 b14fe4bad..45bc89d4e 100644
--- a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
+++ b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
@@ -191,11 +191,26 @@ $`\nabla = \overrightarrow{e_x}\,\dfrac{\partial}{\partial x}+\overrightarrow{e_
 +\overrightarrow{e_z}\,\dfrac{\partial}{\partial z}`$ 
 , or more
 $`\overrightarrow{\nabla} = \overrightarrow{e_x}\,\dfrac{\partial}{\partial x}+\overrightarrow{e_y}\,\dfrac{\partial}{\partial y}
-+\overrightarrow{e_z}\,\dfrac{\partial}{\partial z} `$ 
++\overrightarrow{e_z}\,\dfrac{\partial}{\partial z} `$ <br>
 ES : operador nabla   <br>
 FR : opérateur nabla   <br>
 EN : nabla operator
 
+
+$`\Deltaf = div\,\overrightarrow{grad}\f `$, $`\Deltaf = \overrightarrow{\nabla}\cdot\overrightarrow{\nabla}\,f `$
+ES : operador laplaciana escalar, laplaciana escalar, laplaciana de un campo escalar   <br>
+FR : opérateur laplacien scalaire, laplacien scalaire, laplacien d'un champ scalaire  <br>
+EN : laplacian operator, laplacian of a scalar field
+ES :
+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}`$
+
+$`\Delta = \overrightarrow{grad} div\,\overrightarrow{U} - \overrightarrow{rot}\,\overrightarrow{rot}\,\overrightarrow{U}`$   <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
+
 $`\overrightarrow{grad} f = \nabla f`$, $`\overrightarrow{\nabla}f`$ better, no?   <br>
 ES : gradiente   <br>
 FR : gradient   <br>
@@ -207,7 +222,7 @@ FR : divergence   <br>
 EN : divergence   <br>
 $`div\;\overrightarrow{U}=\lim_{V\leftrightarrow0}\;\dfrac{1}{V}\;\displaystyle\oiint_{S\leftrightarrow V}\overrightarrow{U}\cdot\overrightarrow{dS}`$ 
 
-$`rot\times\overrightarrow{U}`$, but $`\overrightarrow{rot}\times\overrightarrow{U}`$ better, no?   <br>
+$`rot\,\overrightarrow{U}`$, but $`\overrightarrow{rot}\,\overrightarrow{U}`$ better, no?   <br>
 in some English texts : $`curl\times\overrightarrow{U}`$   <br>
 $`\overrightarrow{\nabla}\times\overrightarrow{U}`$ or $`\overrightarrow{\nabla}\land\overrightarrow{U}`$    <br>
 ES : rotacional de un vector  <br>