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Update 2022-03-15 10:07

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Jean-Sébastien
2022-03-15 10:07:27 +01:00
parent 4808df71e6
commit 55f0de8197
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build/c_m_dc_d2.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-03-07 Mon 20:38 -->
<!-- 2022-03-15 Tue 08:10 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1310,10 +1310,6 @@ Table of contents
</summary>
<ul>
<li>
<a href="./d_m.html#d_m">Diagnostics: Mathematical Preliminaries</a><span class="headline-id">d.m</span>
</li>
<li>
<a href="./d_ems.html#d_ems">Diagnostics: Electromagnetostatics</a><span class="headline-id">d.ems</span>
</li>
@@ -1352,6 +1348,10 @@ Table of contents
<li>
<a href="./d_red.html#d_red">Diagnostics: Relativistic Electrodynamics</a><span class="headline-id">d.red</span>
</li>
<li>
<a href="./d_m.html#d_m">Diagnostics: Compendium - Mathematics</a><span class="headline-id">d.m</span>
</li>
</ul>
@@ -1615,9 +1615,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_dc_d2">
</div>
<div id="outline-container-orgc12bd11" class="outline-6">
<h6 id="orgc12bd11"><a href="#orgc12bd11">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orgc12bd11">
<div id="outline-container-orgc162c65" class="outline-6">
<h6 id="orgc162c65"><a href="#orgc162c65">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orgc162c65">
<p>
\({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
@@ -1626,44 +1626,44 @@ given by the Laplacian of the corresponding vector elements.
</div>
</div>
<div id="outline-container-org0ea7ae4" class="outline-6">
<h6 id="org0ea7ae4"><a href="#org0ea7ae4">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org0ea7ae4">
<div id="outline-container-org2f7ef92" class="outline-6">
<h6 id="org2f7ef92"><a href="#org2f7ef92">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org2f7ef92">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-org78d85e1" class="outline-6">
<h6 id="org78d85e1"><a href="#org78d85e1">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org78d85e1">
<div id="outline-container-orgceccef1" class="outline-6">
<h6 id="orgceccef1"><a href="#orgceccef1">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-orgceccef1">
<p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p>
</div>
</div>
<div id="outline-container-orge7f86bf" class="outline-6">
<h6 id="orge7f86bf"><a href="#orge7f86bf">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-orge7f86bf">
<div id="outline-container-orgc07e1dc" class="outline-6">
<h6 id="orgc07e1dc"><a href="#orgc07e1dc">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-orgc07e1dc">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-orgbb8199b" class="outline-6">
<h6 id="orgbb8199b"><a href="#orgbb8199b">Curl of curl</a></h6>
<div class="outline-text-6" id="text-orgbb8199b">
<div class="eqlabel" id="orga59fc73">
<div id="outline-container-org1a67d52" class="outline-6">
<h6 id="org1a67d52"><a href="#org1a67d52">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org1a67d52">
<div class="eqlabel" id="org5d4ff40">
<p>
<a id="curlcurl"></a><a href="./c_m_dc_d2.html#curlcurl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="org384a104">
<div class="alteqlabels" id="orgd2518b8">
</div>
@@ -1694,7 +1694,7 @@ 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: 2022-03-07 Mon 20:38</p>
<p class="date">Created: 2022-03-15 Tue 08:10</p>
<p class="validation"></p>
</div>