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	<id>https://mathresearch.utsa.edu/wiki/index.php?action=history&amp;feed=atom&amp;title=Optimization_Applications</id>
	<title>Optimization Applications - Revision history</title>
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	<updated>2026-04-22T23:03:46Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Optimization_Applications&amp;diff=3444&amp;oldid=prev</id>
		<title>Khanh at 21:22, 3 November 2021</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Optimization_Applications&amp;diff=3444&amp;oldid=prev"/>
		<updated>2021-11-03T21:22:09Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #222; text-align: center;&quot;&gt;Revision as of 21:22, 3 November 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l294&quot; &gt;Line 294:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 294:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Keep in mind, this result is still a derivative. However, we are allowed to model real life scenarios in terms of differential equations. Sometimes, it may be impossible to model situations without differential equations. We are allowed to write our equation like this (physics certainly does not care here). Finally, although this is not ''strictly'' an optimization problem, thinking about in that sense allowed us to obtain a nice rule of the world (a ''law'' in science). We proved this behavior, so it seems light will be consistent according to this equation. This in effect has allowed us to confirm in 2003 that negative index of refraction exists (even through experimental observations) and allowed us to discover properties of spin waves.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;Keep in mind, this result is still a derivative. However, we are allowed to model real life scenarios in terms of differential equations. Sometimes, it may be impossible to model situations without differential equations. We are allowed to write our equation like this (physics certainly does not care here). Finally, although this is not ''strictly'' an optimization problem, thinking about in that sense allowed us to obtain a nice rule of the world (a ''law'' in science). We proved this behavior, so it seems light will be consistent according to this equation. This in effect has allowed us to confirm in 2003 that negative index of refraction exists (even through experimental observations) and allowed us to discover properties of spin waves.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt; &lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;References&lt;/del&gt;==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Licensing&lt;/ins&gt;==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;# Houck, A. A., Brock, J. B., &amp;amp; Chuang, I. L. (2003). Experimental observations of a left-handed material that obeys Snell’s law. Physical Review Letters, 90(13), 137401. Retrieved 25 July 2020 &lt;/del&gt;from &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;http&lt;/del&gt;://&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;feynman&lt;/del&gt;.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;mit&lt;/del&gt;.&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;edu&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;ike&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;homepage&lt;/del&gt;/&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;papers/METAMAT-houck-brock-chuang-experimental-observations-of-&lt;/del&gt;a-&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;left-handed-material-that-obeys-snells-law-prl-v90-p137401-04apr03.pdf.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Content obtained and/or adapted &lt;/ins&gt;from&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;# Stigloher, J., Decker, M., Körner, H. S., Tanabe, K., Moriyama, T., Taniguchi, T., ... &amp;amp; Ono, T. (2016). Snell’s law for spin waves. Physical review letters, 117(3), 037204. Retrieve 22 July 2020 from https://arxiv.org/pdf/1606.02895.pdf.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;* [https&lt;/ins&gt;://&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;en&lt;/ins&gt;.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;wikibooks&lt;/ins&gt;.&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;org&lt;/ins&gt;/&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;wiki&lt;/ins&gt;/&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Calculus&lt;/ins&gt;/&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Optimization Optimization, Wikibooks] under &lt;/ins&gt;a &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;CC BY&lt;/ins&gt;-&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;SA license&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
	<entry>
		<id>https://mathresearch.utsa.edu/wiki/index.php?title=Optimization_Applications&amp;diff=2329&amp;oldid=prev</id>
		<title>Khanh: Created page with &quot; ==Introduction== Optimization is one of the uses of calculus in the real world. Perhaps we are a pizza parlor and wish to maximize profit. Perhaps we have a flat piece of car...&quot;</title>
		<link rel="alternate" type="text/html" href="https://mathresearch.utsa.edu/wiki/index.php?title=Optimization_Applications&amp;diff=2329&amp;oldid=prev"/>
		<updated>2021-10-15T01:42:59Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot; ==Introduction== Optimization is one of the uses of calculus in the real world. Perhaps we are a pizza parlor and wish to maximize profit. Perhaps we have a flat piece of car...&amp;quot;&lt;/p&gt;
&lt;a href=&quot;https://mathresearch.utsa.edu/wiki/index.php?title=Optimization_Applications&amp;amp;diff=2329&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>Khanh</name></author>
		
	</entry>
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