github.com/sentienttechnologies/studio-go-runner@v0.0.0-20201118202441-6d21f2ced8ee/docs/slides/test/examples/math.html (about) 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: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/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>