| JJ Allaire | efa6ad4 | 2016-01-30 13:12:05 -0500 | [diff] [blame] | 1 | <!doctype html> |
| 2 | <html lang="en"> |
| 3 | |
| 4 | <head> |
| 5 | <meta charset="utf-8"> |
| 6 | |
| 7 | <title>reveal.js - Math Plugin</title> |
| 8 | |
| 9 | <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no"> |
| 10 | |
| 11 | <link rel="stylesheet" href="../../css/reveal.css"> |
| 12 | <link rel="stylesheet" href="../../css/theme/night.css" id="theme"> |
| 13 | </head> |
| 14 | |
| 15 | <body> |
| 16 | |
| 17 | <div class="reveal"> |
| 18 | |
| 19 | <div class="slides"> |
| 20 | |
| 21 | <section> |
| 22 | <h2>reveal.js Math Plugin</h2> |
| 23 | <p>A thin wrapper for MathJax</p> |
| 24 | </section> |
| 25 | |
| 26 | <section> |
| 27 | <h3>The Lorenz Equations</h3> |
| 28 | |
| 29 | \[\begin{aligned} |
| 30 | \dot{x} & = \sigma(y-x) \\ |
| 31 | \dot{y} & = \rho x - y - xz \\ |
| 32 | \dot{z} & = -\beta z + xy |
| 33 | \end{aligned} \] |
| 34 | </section> |
| 35 | |
| 36 | <section> |
| 37 | <h3>The Cauchy-Schwarz Inequality</h3> |
| 38 | |
| 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) |
| 41 | </script> |
| 42 | </section> |
| 43 | |
| 44 | <section> |
| 45 | <h3>A Cross Product Formula</h3> |
| 46 | |
| 47 | \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} |
| 48 | \mathbf{i} & \mathbf{j} & \mathbf{k} \\ |
| 49 | \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ |
| 50 | \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 |
| 51 | \end{vmatrix} \] |
| 52 | </section> |
| 53 | |
| 54 | <section> |
| 55 | <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3> |
| 56 | |
| 57 | \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] |
| 58 | </section> |
| 59 | |
| 60 | <section> |
| 61 | <h3>An Identity of Ramanujan</h3> |
| 62 | |
| 63 | \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = |
| 64 | 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} |
| 65 | {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] |
| 66 | </section> |
| 67 | |
| 68 | <section> |
| 69 | <h3>A Rogers-Ramanujan Identity</h3> |
| 70 | |
| 71 | \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = |
| 72 | \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] |
| 73 | </section> |
| 74 | |
| 75 | <section> |
| 76 | <h3>Maxwell’s Equations</h3> |
| 77 | |
| 78 | \[ \begin{aligned} |
| 79 | \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| 80 | \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ |
| 81 | \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} |
| 82 | \] |
| 83 | </section> |
| 84 | |
| 85 | <section> |
| 86 | <section> |
| 87 | <h3>The Lorenz Equations</h3> |
| 88 | |
| 89 | <div class="fragment"> |
| 90 | \[\begin{aligned} |
| 91 | \dot{x} & = \sigma(y-x) \\ |
| 92 | \dot{y} & = \rho x - y - xz \\ |
| 93 | \dot{z} & = -\beta z + xy |
| 94 | \end{aligned} \] |
| 95 | </div> |
| 96 | </section> |
| 97 | |
| 98 | <section> |
| 99 | <h3>The Cauchy-Schwarz Inequality</h3> |
| 100 | |
| 101 | <div class="fragment"> |
| 102 | \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] |
| 103 | </div> |
| 104 | </section> |
| 105 | |
| 106 | <section> |
| 107 | <h3>A Cross Product Formula</h3> |
| 108 | |
| 109 | <div class="fragment"> |
| 110 | \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} |
| 111 | \mathbf{i} & \mathbf{j} & \mathbf{k} \\ |
| 112 | \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ |
| 113 | \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 |
| 114 | \end{vmatrix} \] |
| 115 | </div> |
| 116 | </section> |
| 117 | |
| 118 | <section> |
| 119 | <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3> |
| 120 | |
| 121 | <div class="fragment"> |
| 122 | \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] |
| 123 | </div> |
| 124 | </section> |
| 125 | |
| 126 | <section> |
| 127 | <h3>An Identity of Ramanujan</h3> |
| 128 | |
| 129 | <div class="fragment"> |
| 130 | \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = |
| 131 | 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} |
| 132 | {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] |
| 133 | </div> |
| 134 | </section> |
| 135 | |
| 136 | <section> |
| 137 | <h3>A Rogers-Ramanujan Identity</h3> |
| 138 | |
| 139 | <div class="fragment"> |
| 140 | \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = |
| 141 | \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] |
| 142 | </div> |
| 143 | </section> |
| 144 | |
| 145 | <section> |
| 146 | <h3>Maxwell’s Equations</h3> |
| 147 | |
| 148 | <div class="fragment"> |
| 149 | \[ \begin{aligned} |
| 150 | \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| 151 | \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ |
| 152 | \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} |
| 153 | \] |
| 154 | </div> |
| 155 | </section> |
| 156 | </section> |
| 157 | |
| 158 | </div> |
| 159 | |
| 160 | </div> |
| 161 | |
| 162 | <script src="../../lib/js/head.min.js"></script> |
| 163 | <script src="../../js/reveal.js"></script> |
| 164 | |
| 165 | <script> |
| 166 | |
| 167 | Reveal.initialize({ |
| 168 | history: true, |
| 169 | transition: 'linear', |
| 170 | |
| 171 | math: { |
| 172 | // mathjax: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js', |
| 173 | config: 'TeX-AMS_HTML-full' |
| 174 | }, |
| 175 | |
| 176 | dependencies: [ |
| 177 | { src: '../../lib/js/classList.js' }, |
| 178 | { src: '../../plugin/math/math.js', async: true } |
| 179 | ] |
| 180 | }); |
| 181 | |
| 182 | </script> |
| 183 | |
| 184 | </body> |
| 185 | </html> |