| 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185 | <!doctype html><html lang="en">	<head>		<meta charset="utf-8">		<title>reveal.js - Math Plugin</title>		<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">		<link rel="stylesheet" href="../../css/reveal.min.css">		<link rel="stylesheet" href="../../css/theme/night.css" id="theme">	</head>	<body>		<div class="reveal">			<div class="slides">				<section>					<h2>reveal.js Math Plugin</h2>					<p>A thin wrapper for MathJax</p>				</section>				<section>					<h3>The Lorenz Equations</h3>					\[\begin{aligned}					\dot{x} & = \sigma(y-x) \\					\dot{y} & = \rho x - y - xz \\					\dot{z} & = -\beta z + xy					\end{aligned} \]				</section>				<section>					<h3>The Cauchy-Schwarz Inequality</h3>					<script type="math/tex; mode=display">						\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)					</script>				</section>				<section>					<h3>A Cross Product Formula</h3>					\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}					\mathbf{i} & \mathbf{j} & \mathbf{k} \\					\frac{\partial X}{\partial u} &  \frac{\partial Y}{\partial u} & 0 \\					\frac{\partial X}{\partial v} &  \frac{\partial Y}{\partial v} & 0					\end{vmatrix}  \]				</section>				<section>					<h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>					\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]				</section>				<section>					<h3>An Identity of Ramanujan</h3>					\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =					1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}					{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]				</section>				<section>					<h3>A Rogers-Ramanujan Identity</h3>					\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =					\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]				</section>				<section>					<h3>Maxwell’s Equations</h3>					\[  \begin{aligned}					\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\					\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\					\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}					\]				</section>				<section>					<section>						<h3>The Lorenz Equations</h3>						<div class="fragment">							\[\begin{aligned}							\dot{x} & = \sigma(y-x) \\							\dot{y} & = \rho x - y - xz \\							\dot{z} & = -\beta z + xy							\end{aligned} \]						</div>					</section>					<section>						<h3>The Cauchy-Schwarz Inequality</h3>						<div class="fragment">							\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]						</div>					</section>					<section>						<h3>A Cross Product Formula</h3>						<div class="fragment">							\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}							\mathbf{i} & \mathbf{j} & \mathbf{k} \\							\frac{\partial X}{\partial u} &  \frac{\partial Y}{\partial u} & 0 \\							\frac{\partial X}{\partial v} &  \frac{\partial Y}{\partial v} & 0							\end{vmatrix}  \]						</div>					</section>					<section>						<h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>						<div class="fragment">							\[P(E)   = {n \choose k} p^k (1-p)^{ n-k} \]						</div>					</section>					<section>						<h3>An Identity of Ramanujan</h3>						<div class="fragment">							\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =							1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}							{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]						</div>					</section>					<section>						<h3>A Rogers-Ramanujan Identity</h3>						<div class="fragment">							\[  1 +  \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =							\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]						</div>					</section>					<section>						<h3>Maxwell’s Equations</h3>						<div class="fragment">							\[  \begin{aligned}							\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\							\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\							\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}							\]						</div>					</section>				</section>			</div>		</div>		<script src="../../lib/js/head.min.js"></script>		<script src="../../js/reveal.min.js"></script>		<script>			Reveal.initialize({				history: true,				transition: 'linear',				math: {					// mathjax: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js',					config: 'TeX-AMS_HTML-full'				},				dependencies: [					{ src: '../../lib/js/classList.js' },					{ src: '../../plugin/math/math.js', async: true }				]			});		</script>	</body></html>
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