From 6a1d2481c81e84b7a02dd37b81f381dd69610a2f Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Tue, 19 Nov 2019 18:54:12 +0100 Subject: [PATCH] Update textbook.en.md --- .../textbook.en.md | 20 +++++++++++++++++-- 1 file changed, 18 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 57b2b1f4e..6ac40a84c 100644 --- a/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md +++ b/10.brainstorming-innovative-courses/intercambio-curso-electromagnetismo/textbook.en.md @@ -758,17 +758,33 @@ Mecánica newtoniana : espacio y el tiempo son desacoplados $`\Longrightarrow`$ $`\displaystyle\iint_S \overrightarrow{rot}\,\overrightarrow{E}\cdot \overrightarrow{dS} = - \dfrac{\partial}{\partial t} \left( \displaystyle\iint_S \overrightarrow{B}\cdot \overrightarrow{dS}\right)`$ +Stokes' theorem = + +for all vectorial field $`\vec{X}`$, + +$`\displaystyle\iint_{S\,orient.} \;\overrightarrow{rot}\;\overrightarrow{X} \cdot dS += \displaystyle \oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{X}\cdot\overrightarrow{dl}`$ + +$`\displaystyle\iint_{S\,orient.} \overrightarrow{rot} \,\overrightarrow{E}\cdot \overrightarrow{dS} += \displaystyle \oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{E}\cdot\overrightarrow{dl} += -\displaystyle\iint_{S \leftrightarrow \tau} \dfrac{\partial \overrightarrow{B}}{\partial t}\cdot \overrightarrow{dS}`$ + + + + Ostrogradsky’s theorem = divergence theorem (= Gauss's theorem) : for all vectorial field $`\vec{X}`$, -$`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle \oiint_{S\leftrightarrow\tau} \overrightarrow{X}\cdot\overrightarrow{dS}`$ +$`\displaystyle\iiint_{\tau} div\;\overrightarrow{X} \cdot d\tau = \displaystyle +\oiint_{S\leftrightarrow\tau} \overrightarrow{X}\cdot\overrightarrow{dS}`$ Stokes' theorem = for all vectorial field $`\vec{X}`$, -$`\displaystyle\iint_{S\,orient.} \;\overrightarrow{rot}\;\overrightarrow{X} \cdot dS = \displaystyle \oint_{\Gamma\,orient.\overrightarrow{S}} \overrightarrow{X}\cdot\overrightarrow{dl}`$ +$`\displaystyle\iint_{S\,orient.} \;\overrightarrow{rot}\;\overrightarrow{X} \cdot dS = \displaystyle +\oint_{\Gamma\,orient.\leftrightarrow S} \overrightarrow{X}\cdot\overrightarrow{dl}`$