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Update 2022-02-08 17:21

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Jean-Sébastien
2022-02-08 17:21:33 +01:00
parent 077433c40a
commit 3454aba504
207 changed files with 1882 additions and 1097 deletions
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build/c_m_dc_d2.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 06:55 -->
<!-- 2022-02-08 Tue 17:21 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -272,6 +272,10 @@ Table of contents
</summary>
<ul>
<li>
<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
</li>
<li>
<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
</li>
@@ -736,7 +740,7 @@ Table of contents
</li>
<li>
<a href="./emsm_esm_d.html#emsm_esm_d">Dielectrics</a><span class="headline-id">emsm.esm.d</span>
<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
</li>
<li>
@@ -1620,9 +1624,9 @@ Table of contents
<div class="outline-text-5" id="text-c_m_dc_d2">
</div>
<div id="outline-container-orgc3b89bb" class="outline-6">
<h6 id="orgc3b89bb"><a href="#orgc3b89bb">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-orgc3b89bb">
<div id="outline-container-org5fd48d1" class="outline-6">
<h6 id="org5fd48d1"><a href="#org5fd48d1">Divergence of gradient</a></h6>
<div class="outline-text-6" id="text-org5fd48d1">
<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
@@ -1631,36 +1635,36 @@ given by the Laplacian of the corresponding vector elements.
</div>
</div>
<div id="outline-container-org5caf3f5" class="outline-6">
<h6 id="org5caf3f5"><a href="#org5caf3f5">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org5caf3f5">
<div id="outline-container-org41a3448" class="outline-6">
<h6 id="org41a3448"><a href="#org41a3448">Curl of a gradient</a></h6>
<div class="outline-text-6" id="text-org41a3448">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-org4f9116a" class="outline-6">
<h6 id="org4f9116a"><a href="#org4f9116a">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org4f9116a">
<div id="outline-container-org6c4b5a7" class="outline-6">
<h6 id="org6c4b5a7"><a href="#org6c4b5a7">Gradient of the divergence</a></h6>
<div class="outline-text-6" id="text-org6c4b5a7">
<p>
\({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics. No special name.
</p>
</div>
</div>
<div id="outline-container-org2c1c081" class="outline-6">
<h6 id="org2c1c081"><a href="#org2c1c081">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org2c1c081">
<div id="outline-container-org68b62ab" class="outline-6">
<h6 id="org68b62ab"><a href="#org68b62ab">Divergence of a curl</a></h6>
<div class="outline-text-6" id="text-org68b62ab">
<p>
This always vanishes.
</p>
</div>
</div>
<div id="outline-container-orgc977e97" class="outline-6">
<h6 id="orgc977e97"><a href="#orgc977e97">Curl of curl</a></h6>
<div class="outline-text-6" id="text-orgc977e97">
<div id="outline-container-org62690be" class="outline-6">
<h6 id="org62690be"><a href="#org62690be">Curl of curl</a></h6>
<div class="outline-text-6" id="text-org62690be">
<p>
\[
{\boldsymbol \nabla} \times ({\boldsymbol \nabla} \times {\bf v}) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v}) - {\boldsymbol \nabla}^2 {\bf v}
@@ -1674,7 +1678,7 @@ This always vanishes.
<hr><div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-08 Tue 06:55</p>
<p class="date">Created: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
</div>