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Update 2022-02-14 06:33

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Jean-Sébastien
2022-02-14 06:33:37 +01:00
parent f8446c1405
commit 4cfe8cef59
204 changed files with 1839 additions and 941 deletions
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build/c_m_dc_d2.html
+19 -17
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-10 Thu 08:32 -->
<!-- 2022-02-13 Sun 21:20 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1599,9 +1599,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_dc_d2">
</div>
<div id="outline-container-orgd5309ec" class="outline-6">
<h6 id="orgd5309ec"><a href="#orgd5309ec">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orgd5309ec">
<div id="outline-container-orgbe5f73d" class="outline-6">
<h6 id="orgbe5f73d"><a href="#orgbe5f73d">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orgbe5f73d">
<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
@@ -1610,36 +1610,36 @@ given by the Laplacian of the corresponding vector elements.
</div>
</div>
<div id="outline-container-org3f8f01e" class="outline-6">
<h6 id="org3f8f01e"><a href="#org3f8f01e">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org3f8f01e">
<div id="outline-container-orgee1ca6a" class="outline-6">
<h6 id="orgee1ca6a"><a href="#orgee1ca6a">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-orgee1ca6a">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-org86a1e1f" class="outline-6">
<h6 id="org86a1e1f"><a href="#org86a1e1f">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org86a1e1f">
<div id="outline-container-org2789da2" class="outline-6">
<h6 id="org2789da2"><a href="#org2789da2">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org2789da2">
<p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p>
</div>
</div>
<div id="outline-container-orgdca9d9a" class="outline-6">
<h6 id="orgdca9d9a"><a href="#orgdca9d9a">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-orgdca9d9a">
<div id="outline-container-org62ec566" class="outline-6">
<h6 id="org62ec566"><a href="#org62ec566">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org62ec566">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-org613cb02" class="outline-6">
<h6 id="org613cb02"><a href="#org613cb02">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org613cb02">
<div id="outline-container-org5cd2844" class="outline-6">
<h6 id="org5cd2844"><a href="#org5cd2844">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org5cd2844">
<p>
\[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
@@ -1651,6 +1651,8 @@ This always vanishes.
</div>
<br><ul class="navigation-links"><li>Prev:&nbsp;<a href="c_m_dc_pr.html">Product Rules&emsp;<small>[c.m.dc.pr]</small></a></li><li>Next:&nbsp;<a href="c_m_ic.html">Integral Calculus&emsp;<small>[c.m.ic]</small></a></li><li>Up:&nbsp;<a href="c_m_dc.html">Differential Calculus&emsp;<small>[c.m.dc]</small></a></li></ul>
<br>
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
@@ -1664,7 +1666,7 @@ 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: 2022-02-10 Thu 08:32</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="validation"></p>
</div>