From fc259092cfd68d1ab218e5fef6dbcbece8d5654a Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Tue, 19 Nov 2019 17:30:02 +0100
Subject: [PATCH] Update textbook.en.md

---
 .../textbook.en.md                            | 20 ++++++-------------
 1 file changed, 6 insertions(+), 14 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 372b2bd75..779a91b32 100644
--- a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
+++ b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md
@@ -637,7 +637,7 @@ local (magnétostatique)
 
 $`\overrightarrow{rot}\,\overrightarrow{B}=\mu_0 \cdot \overrightarrow{j}`$
 
-Electromagnétisme dans le vide :
+local (électromagnetism)
 
 $`\overrightarrow{rot}\,\overrightarrow{B}=\mu_0 \cdot \overrightarrow{j}\,+ \, \epsilon_0\mu_0 \cdot \dfrac{\partial \overrightarrow{E}}{\partial t}`$$`=\mu_0 \cdot \overrightarrow{j}\,+ \, \dfrac{1}{c^2} \cdot \dfrac{\partial \overrightarrow{E}}{\partial t}`$$`=\mu_0 \cdot \overrightarrow{j}\,+ \mu_0 \cdot \overrightarrow{j_D}`$$` = \mu_0 \cdot (\overrightarrow{j}+\overrightarrow{j_D})`$
 
@@ -755,25 +755,17 @@ $`\displaystyle\iint_S \overrightarrow{rot} \,\overrightarrow{E}\cdot \overright
 
 Mecánica newtoniana : espacio y el tiempo son desacoplados $`\Longrightarrow`$ orden de integración / derivación entre variables de espacio y tiempo no importa.
 
-$`\displaystyle\iint_S \overrightarrow{rot}\,\overrightarrow{E}\cdot \overrightarrow{dS} = - \dfrac{\partial}{\partial t} \left( \displaystyle\iint_S \overrightarrow{B}\cdot \overrightarrow{dS}\right)`$
+$`\displaystyle\iint_S \overrightarrow{rot}\,\overrightarrow{E}\cdot \overrightarrow{dS} 
+= - \dfrac{\partial}{\partial t} \left( \displaystyle\iint_S \overrightarrow{B}\cdot \overrightarrow{dS}\right)`$
 
-Ostrogradsky’s theorem : for all vectorial field $`\vec{X}`$, 
+Ostrogradsky’s theorem = divergence theorem (= Gauss's theorem) :
 
+for all vectorial field $`\vec{X}`$, 
 
-Con los vectores de intensidad de campo eléctrico $`\overrightarrow{E}`$ y magnético `\overrightarrow{H}`$
-Avec les vecteurs d'excitation électrique $`\overrightarrow{E}`$ et magnétique `\overrightarrow{H}`$
-    
-$`\displaystyle\oiint_S\overrightarrow{E}\cdot\overrightarrow{dS}=\dfrac{Q_{int}}{\epsilon_0}`$
-$`=\dfrac{1}{\epsilon_0} \cdot \displaystyle\iiint_{\tau\leftrightarrow S} \rho \cdot d\tau`$
+$`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau= \displaystyle\oiint_{S \leftrightarrow \tau}\overrightarrow{X}}\cdot\overrightarrow{dS}`$
 
-$`\displaystyle\oiint_S\overrightarrow{H}\cdot\overrightarrow{dS}=0`$
 
-$`\displaystyle\iiint_{\tau} div\overrightarrow{E} \cdot d\tau= \displaystyle\iiint_{\tau}
-\dfrac{\rho}{\epsilon_0} \cdot d\tau = \dfrac{1}{\epsilon_0} \cdot \iiint_{\tau} \rho 
-\cdot d\tau = \dfrac{Q_{int}}{\epsilon_0} `$
 
-$`\displaystyle\iint_S \overrightarrow{rot} \,\overrightarrow{E}\cdot \overrightarrow{dS}
-= -\displaystyle\iint_{S \leftrightarrow \tau} \mu_0 \dfrac{\partial \overrightarrow{H}}{\partial t}\cdot \overrightarrow{dS}`$