math.html (5641B)
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 <h3>TeX Macros</h3> 87 88 Here is a common vector space: 89 \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\] 90 used in functional analysis. 91 </section> 92 93 <section> 94 <section> 95 <h3>The Lorenz Equations</h3> 96 97 <div class="fragment"> 98 \[\begin{aligned} 99 \dot{x} & = \sigma(y-x) \\ 100 \dot{y} & = \rho x - y - xz \\ 101 \dot{z} & = -\beta z + xy 102 \end{aligned} \] 103 </div> 104 </section> 105 106 <section> 107 <h3>The Cauchy-Schwarz Inequality</h3> 108 109 <div class="fragment"> 110 \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] 111 </div> 112 </section> 113 114 <section> 115 <h3>A Cross Product Formula</h3> 116 117 <div class="fragment"> 118 \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} 119 \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 120 \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ 121 \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 122 \end{vmatrix} \] 123 </div> 124 </section> 125 126 <section> 127 <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3> 128 129 <div class="fragment"> 130 \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] 131 </div> 132 </section> 133 134 <section> 135 <h3>An Identity of Ramanujan</h3> 136 137 <div class="fragment"> 138 \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 139 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} 140 {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] 141 </div> 142 </section> 143 144 <section> 145 <h3>A Rogers-Ramanujan Identity</h3> 146 147 <div class="fragment"> 148 \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = 149 \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] 150 </div> 151 </section> 152 153 <section> 154 <h3>Maxwell’s Equations</h3> 155 156 <div class="fragment"> 157 \[ \begin{aligned} 158 \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ 159 \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ 160 \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} 161 \] 162 </div> 163 </section> 164 165 <section> 166 <h3>TeX Macros</h3> 167 168 Here is a common vector space: 169 \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\] 170 used in functional analysis. 171 </section> 172 </section> 173 174 </div> 175 176 </div> 177 178 <script src="../../js/reveal.js"></script> 179 180 <script> 181 182 Reveal.initialize({ 183 history: true, 184 transition: 'linear', 185 186 math: { 187 // mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js', 188 config: 'TeX-AMS_HTML-full', 189 TeX: { 190 Macros: { 191 R: '\\mathbb{R}', 192 set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ] 193 } 194 } 195 }, 196 197 dependencies: [ 198 { src: '../../plugin/math/math.js', async: true } 199 ] 200 }); 201 202 </script> 203 204 </body> 205 </html>