7 <title>reveal.js - Math Plugin</title>
9 <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
11 <link rel="stylesheet" href="../../css/reveal.css">
12 <link rel="stylesheet" href="../../css/theme/night.css" id="theme">
22 <h2>reveal.js Math Plugin</h2>
23 <p>A thin wrapper for MathJax</p>
27 <h3>The Lorenz Equations</h3>
30 \dot{x} & = \sigma(y-x) \\
31 \dot{y} & = \rho x - y - xz \\
32 \dot{z} & = -\beta z + xy
37 <h3>The Cauchy-Schwarz Inequality</h3>
39 <script type="math/tex; mode=display">
40 \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)
45 <h3>A Cross Product Formula</h3>
47 \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
48 \mathbf{i} & \mathbf{j} & \mathbf{k} \\
49 \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
50 \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
55 <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
57 \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
61 <h3>An Identity of Ramanujan</h3>
63 \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
64 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
65 {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
69 <h3>A Rogers-Ramanujan Identity</h3>
71 \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
72 \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
76 <h3>Maxwell’s Equations</h3>
79 \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 \\
80 \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
81 \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
87 <h3>The Lorenz Equations</h3>
89 <div class="fragment">
91 \dot{x} & = \sigma(y-x) \\
92 \dot{y} & = \rho x - y - xz \\
93 \dot{z} & = -\beta z + xy
99 <h3>The Cauchy-Schwarz Inequality</h3>
101 <div class="fragment">
102 \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
107 <h3>A Cross Product Formula</h3>
109 <div class="fragment">
110 \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
111 \mathbf{i} & \mathbf{j} & \mathbf{k} \\
112 \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
113 \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
119 <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
121 <div class="fragment">
122 \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
127 <h3>An Identity of Ramanujan</h3>
129 <div class="fragment">
130 \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
131 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
132 {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
137 <h3>A Rogers-Ramanujan Identity</h3>
139 <div class="fragment">
140 \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
141 \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
146 <h3>Maxwell’s Equations</h3>
148 <div class="fragment">
150 \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 \\
151 \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
152 \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
162 <script src="../../lib/js/head.min.js"></script>
163 <script src="../../js/reveal.js"></script>
169 transition: 'linear',
172 // mathjax: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js',
173 config: 'TeX-AMS_HTML-full'
177 { src: '../../lib/js/classList.js' },
178 { src: '../../plugin/math/math.js', async: true }