From a752601717ae09b84924990bf5df132ca752605c Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Sun, 30 Aug 2020 11:08:35 +0200 Subject: [PATCH] Update textbook.fr.md --- .../04.reference-frames-coordinate-systems/textbook.fr.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md index 939a69fcf..9a939e5e4 100644 --- a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md +++ b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md @@ -243,17 +243,17 @@ $`\quad\overrightarrow{dS}\quad`$,$`\quad\overrightarrow{d^2S}\quad`$ [FR] et les **éléments vectoriels de surface $`\overrightarrow{dA}`$** correspondants sont :
[EN] and the corresponding **vector surface elements $`\overrightarrow{dA}`$** are :

$`d\overrightarrow{A_{xy}}=\pm\;\partial\overrightarrow{OM}_x\land\partial\overrightarrow{OM}_y`$ -$`\pm\;\overrightarrow{dl_x}\land\overrightarrow{dl_y}`$ +$`=\pm\;\overrightarrow{dl_x}\land\overrightarrow{dl_y}`$ $`=\pm\; (dl_x\;\overrightarrow{e_x})\land(dl_y\;\overrightarrow{e_y})`$ $`=\pm\; dl_x\;dl_y\;(\overrightarrow{e_x}\land\overrightarrow{e_y})`$ $`= \pm \; dx\;dy\;\overrightarrow{e_z}`$

$`d\overrightarrow{A_{xz}}=\pm\;\partial\overrightarrow{OM}_x\land\partial\overrightarrow{OM}_z`$ -$`\pm\;\overrightarrow{dl_x}\land\overrightarrow{dl_z}`$ +$`=\pm\;\overrightarrow{dl_x}\land\overrightarrow{dl_z}`$ $`=\pm\; (dl_x\;\overrightarrow{e_x})\land(dl_z\;\overrightarrow{e_z})`$ $`=\pm\; dl_x\;dl_z\;(\overrightarrow{e_x}\land\overrightarrow{e_z})`$ $`=\mp\; dx\;dy\;\overrightarrow{e_z}`$

$`d\overrightarrow{A_{yz}}=\pm\;\partial\overrightarrow{OM}_y\land\partial\overrightarrow{OM}_z`$ -$`\pm\;\overrightarrow{dl_y}\land\overrightarrow{dl_z}`$ +$`=\pm\;\overrightarrow{dl_y}\land\overrightarrow{dl_z}`$ $`=\pm\; (dl_y\;\overrightarrow{e_y})\land(dl_z\;\overrightarrow{e_z})`$ $`=\pm\; dl_y\;dl_z\;(\overrightarrow{e_y}\land\overrightarrow{e_z})`$ $`=\pm\; dy\;dz\;\overrightarrow{e_x}`$