Commit d489528c authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent d64aace0
Pipeline #15691 canceled with stage
......@@ -340,24 +340,25 @@ $`\quad = A\cdot
<br>
* soit en *notation réelle* :
<br>
1D : *$`\mathbf{U(x,t)=A\cdot cos\,(\omega t - k x + \varphi)}`$*
1D : *$`\quad\mathbf{U(x,t)=A\cdot cos\,(\omega t - k x + \varphi)}`$*
<br>
3D : *$`\mathbf{U(x,t)=A\cdot cos\,(\omega t - \vec{k}\cdot\vec{r} + \varphi)}`$*
3D : *$`\quad\mathbf{U(x,t)=A\cdot cos\,(\omega t - \vec{k}\cdot\vec{r} + \varphi)}`$*
* soit en **notation complexe** :
<br>
1D : **$`\mathbf{\underline{U}(x,t)=A\cdot e^{\,i\,(\omega t - k x + \varphi)}}`$**
1D : **$`\quad\large{\mathbf{\underline{U}(x,t)=A\cdot e^{\,i\,(\omega t - k x + \varphi)}}}`$**
<br>
3D : $`\begin{align}\mathbf{\color{brown}{\underline{U}(x,t)&=A\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r} + \varphi)}}}\\
3D : $`\begin{align}
\mathbf{\color{brown}{\quad\underline{U}(x,t)&=A\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r} + \varphi)} }}\\
&=A\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r})}\cdot e^{\,i\varphi)}\\
&=A\cdot e^{\,i\varphi)}\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r})}\\
&=\mathbf{\color{brown}{\underline{A}\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r})}}}\\
&\quad\quad\text{avec }\mathbf{\color{blue}{\underline{A}=A\; e^{\,i\varphi)}}}\\
&\quad\quad\quad\color{blue}{\text{amplitude complexe}\end{align}`$
&=\mathbf{\color{brown}{\underline{A}\cdot e^{\,i\,(\omega t - \vec{k}\cdot\vec{r})} }}\\
&\quad\quad\text{avec }\mathbf{\color{blue}{\underline{A}=A\; e^{\,i\varphi} }}\\
&\quad\quad\quad\color{blue}{\text{amplitude complexe}}\end{align}`$
* L'**onde physique** $`U(x,t)`$ est **réelle** et s'exprime comme la *partie réelle de l'onde complexe* :
<br>
**$`\mathbf{U(x,t) = \mathscr{Re}\underline{U}(x,t})}`$**
**$`\mathbf{U(x,t) = \mathscr{Re}\big(\underline{U}(x,t})\big)}`$**
......
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