Commit 6203bc2a authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 3c7a4ee8
Pipeline #15708 canceled with stage
......@@ -342,14 +342,11 @@ $`\forall \alpha \in \mathbb{R}\;,\,`$ **$`\large{exp{\,\alpha} = cos \,\alpha +
3D : *$`\quad\large{\boldsymbol{\mathbf{U(\vec{r},t)=A\cdot cos\,(\omega t - \vec{k}\cdot\vec{r} + \varphi)}}}`$*
* soit en **notation complexe** :
1D : $`\begin{align}
\quad\color{brown}{\large{\boldsymbol{\mathbf{\underline{U}(x,t)}}}} &= A\cdot e^{\,i\,(\omega t - k x + \varphi)}\\
&\color{blue}{\scriptsize{\quad\quad exp(a+b) = exp(a)\times exp(b)}}\\
&\\
&=A\;e^{\,i\,\varphi}\cdot e^{\,i\,(\omega t - kx)}\\
&\\
&\color{brown}{\boldsymbol{\mathbf{\large{=\underline{A}\cdot e^{\,i\,(\omega t - kx)}}}}}
\end{align}`$
1D : **$`\quad\large{\boldsymbol{\mathbf{\underline{U}(x,t)}}`$** $`\;= A\cdot exp\,[\,i\,(\underbrace{\omega t - k x + \varphi}_{\color{blue}{exp(a+b) = exp(a)\times exp(b)}})\,]`$
<br>
$`\quad\quad\quad\quad\quad\quad =\underbrace{A\;e^{\,i\,\varphi}}_{\color{blue}{\underline{A}=A\; exp (\,i\varphi))}}\cdot exp\,[\,i\,(\omega t - kx)\,]`$
<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>
......
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