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Update 2022-02-14 20:42

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Jean-Sébastien
2022-02-14 20:42:37 +01:00
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commit 09a8ba5fb6
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build/c_m_dc_d2.html
+17 -17
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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>
@@ -1599,9 +1599,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_dc_d2">
</div>
<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">
<div id="outline-container-org909c107" class="outline-6">
<h6 id="org909c107"><a href="#org909c107">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-org909c107">
<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-orgee1ca6a" class="outline-6">
<h6 id="orgee1ca6a"><a href="#orgee1ca6a">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-orgee1ca6a">
<div id="outline-container-org9576a42" class="outline-6">
<h6 id="org9576a42"><a href="#org9576a42">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org9576a42">
<p>
This always vanishes.
</p>
</div>
</div>
<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">
<div id="outline-container-org9eefe8b" class="outline-6">
<h6 id="org9eefe8b"><a href="#org9eefe8b">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org9eefe8b">
<p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p>
</div>
</div>
<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">
<div id="outline-container-org0de49a1" class="outline-6">
<h6 id="org0de49a1"><a href="#org0de49a1">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org0de49a1">
<p>
This always vanishes.
</p>
</div>
</div>
<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">
<div id="outline-container-org937d8f6" class="outline-6">
<h6 id="org937d8f6"><a href="#org937d8f6">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org937d8f6">
<p>
\[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
@@ -1666,7 +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: 2022-02-13 Sun 21:20</p>
<p class="date">Created: 2022-02-14 Mon 20:35</p>
<p class="validation"></p>
</div>