Commit ae3e1f33 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent e4cf95fa
Pipeline #13291 canceled with stage
...@@ -418,13 +418,18 @@ $`\begin{align} ...@@ -418,13 +418,18 @@ $`\begin{align}
$`\color{brown}{\mathbf{\; = X_{\alpha}\,dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}}}`$ $`\color{brown}{\mathbf{\; = X_{\alpha}\,dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}}}`$
Par ailleurs,$`\phi`$ étant un champ scalaire, sa différentielle exprimée en coordonnées $`(\alpha\,,\beta\,,\gamma)`$ s'écrit : Par ailleurs,$`\phi`$ étant un champ scalaire, sa différentielle exprimée en fonction des $`(d\alpha\,,d\beta\,,d\gamma)`$ s'écrit :
<!--------------------- <!---------------------
$`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\alpha} + \left.\dfrac{\partial \phi}{\partial \beta}\right|_M\cdot dl_{\beta} + \left.\dfrac{\partial \phi}{\partial \gamma}\right|_M\cdot dl_{\gamma}}`$ $`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\alpha} + \left.\dfrac{\partial \phi}{\partial \beta}\right|_M\cdot dl_{\beta} + \left.\dfrac{\partial \phi}{\partial \gamma}\right|_M\cdot dl_{\gamma}}`$
---------------------> --------------------->
$`\mathbf{d\phi=\dfrac{\partial \phi}{\partial \alpha}\cdot d\alpha + \dfrac{\partial \phi}{\partial \beta}\cdot d\beta + \dfrac{\partial \phi}{\partial \gamma}\cdot d\gamma}`$ $`\mathbf{d\phi}=\dfrac{\partial \phi}{\partial \alpha}\cdot d\alpha + \dfrac{\partial \phi}{\partial \beta}\cdot d\beta + \dfrac{\partial \phi}{\partial \gamma}\cdot d\gamma`$
$`\mathbf{d\phi}=
\dfrac{\partial \phi}{\partial dl_{\alpha}}\,\dfrac{\partial dl_{\alpha}}{\partial \alpha}\, d\alpha}
+\dfrac{\partial \phi}{\partial dl_{\beta}}\,\dfrac{\partial dl_{\beta}}{\partial \beta}\, d\beta}
+\dfrac{\partial \phi}{\partial dl_{\gamma}}\,\dfrac{\partial dl_{\gamma}}{\partial \gamma}\, d\gamma}`$
......
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