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Update 2022-02-14 20:42

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Jean-Sébastien
2022-02-14 20:42:37 +01:00
parent 4cfe8cef59
commit 09a8ba5fb6
204 changed files with 1968 additions and 1206 deletions
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build/c_m_uf_sph.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-13 Sun 21:20 -->
<!-- 2022-02-14 Mon 20:35 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1600,21 +1600,21 @@ Table of contents
\begin{align*}
\mbox{Gradient:}
&amp;{\boldsymbol \nabla} T = \frac{\partial T}{\partial r} \hat{\boldsymbol r} + \frac{1}{r} \frac{\partial T}{\partial \theta} \hat{\boldsymbol \theta}
+ \frac{1}{r\sin \theta} \frac{\partial T}{\partial \phi} \hat{\boldsymbol \phi}.
+ \frac{1}{r\sin \theta} \frac{\partial T}{\partial \varphi} \hat{\boldsymbol \varphi}.
\nonumber \\
\mbox{Divergence:}
&amp;{\boldsymbol \nabla} \cdot {\bf v} = \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 v_r) + \frac{1}{r\sin \theta} \frac{\partial}{\partial \theta} (\sin\theta v_{\theta})
+ \frac{1}{r \sin \theta} \frac{\partial v_{\phi}}{\partial \phi}
+ \frac{1}{r \sin \theta} \frac{\partial v_{\varphi}}{\partial \varphi}
\nonumber\\
\mbox{Curl:}
&amp;{\boldsymbol \nabla} \times {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (\sin \theta v_{\phi}) - \frac{\partial v_{\theta}}{\partial \phi} \right] \hat{\bf r}
+ \frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \phi} - \frac{\partial}{\partial r} (r v_{\phi}) \right] \hat{\boldsymbol \theta}
+ \frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{\theta}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \phi}
&amp;{\boldsymbol \nabla} \times {\bf v} = \frac{1}{r\sin \theta} \left[ \frac{\partial}{\partial \theta} (\sin \theta v_{\varphi}) - \frac{\partial v_{\theta}}{\partial \varphi} \right] \hat{\bf r}
+ \frac{1}{r} \left[ \frac{1}{\sin \theta} \frac{\partial v_r}{\partial \varphi} - \frac{\partial}{\partial r} (r v_{\varphi}) \right] \hat{\boldsymbol \theta}
+ \frac{1}{r} \left[ \frac{\partial}{\partial r} (r v_{\theta}) - \frac{\partial v_r}{\partial \theta} \right] \hat{\boldsymbol \varphi}
\nonumber\\
\mbox{Laplacian:}
&amp;{\boldsymbol \nabla}^2 T = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial T}{\partial r}\right)
+ \frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( \sin \theta \frac{\partial T}{\partial \theta}\right)
+ \frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 T}{\partial \phi^2}
+ \frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 T}{\partial \varphi^2}
\end{align*}
</div>
</div>
@@ -1636,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="date">Created: 2022-02-14 Mon 20:35</p>
<p class="validation"></p>
</div>