Commit 65d74cda authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 6203bc2a
Pipeline #15709 canceled with stage
......@@ -342,15 +342,15 @@ $`\forall \alpha \in \mathbb{R}\;,\,`$ **$`\large{exp{\,\alpha} = cos \,\alpha +
3D : *$`\quad\large{\boldsymbol{\mathbf{U(\vec{r},t)=A\cdot cos\,(\omega t - \vec{k}\cdot\vec{r} + \varphi)}}}`$*
* soit en **notation complexe** :
1D : **$`\quad\large{\boldsymbol{\mathbf{\underline{U}(x,t)}}`$** $`\;= A\cdot exp\,[\,i\,(\underbrace{\omega t - k x + \varphi}_{\color{blue}{exp(a+b) = exp(a)\times exp(b)}})\,]`$
1D : **$`\quad\large{\boldsymbol{\mathbf{\underline{U}(x,t)}}}`$** $`\;= A\cdot \underbrace{exp\,[\,i\,(\omega t - k x + \varphi}_{\color{blue}{exp(a+b) = exp(a)\times exp(b)})\,]}`$
<br>
$`\quad\quad\quad\quad\quad\quad =\underbrace{A\;e^{\,i\,\varphi}}_{\color{blue}{\underline{A}=A\; exp (\,i\varphi))}}\cdot exp\,[\,i\,(\omega t - kx)\,]`$
$`\quad\quad\quad\quad\quad\quad =\underbrace{A\;e^{\,i\,\varphi}}_{\color{blue}{\underline{A}=A\; e^{\,i\,\varphi}}\cdot exp\,[\,i\,(\omega t - kx)\,]`$
<br>
**$`\quad\quad\quad\quad\quad\quad\boldsymbol{\mathbf{\large{=\underline{A}\cdot e^{\,i\,(\omega t - kx)}}}}`$**
<br>
3D : **$`\quad\large{\boldsymbol{\mathbf{\underline{U}(\vec{r},t)=\underline{A}\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r})}}}}`$**
<br>
*$`\quad\quad\quad\quad\quad\quad`$ avec *$`\boldsymbol{\large{\mathbf{\underline{A}=A\; e^{\,i\varphi}}}}`$ : amplitude complexe*.
$`\quad\quad\quad\quad\quad\quad`$ avec *$`\boldsymbol{\large{\mathbf{\underline{A}=A\; e^{\,i\varphi}}}}`$ : amplitude complexe*.
* L'**onde $`U(x,t)`$** est **réelle** et s'exprime comme la *partie réelle de l'onde complexe $`\underline{U}(x,t)`$*.
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