| 1 | <!DOCTYPE html> |
| 2 | <html lang="en"> |
| 3 | <head> |
| 4 | <meta charset="utf-8" /> |
| 5 | |
| 6 | <title>reveal.js - Math Plugin</title> |
| 7 | |
| 8 | <meta |
| 9 | name="viewport" |
| 10 | content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no" |
| 11 | /> |
| 12 | |
| 13 | <link rel="stylesheet" href="../dist/reveal.css" /> |
| 14 | <link rel="stylesheet" href="../dist/theme/night.css" id="theme" /> |
| 15 | </head> |
| 16 | |
| 17 | <body> |
| 18 | <div class="reveal"> |
| 19 | <!-- prettier-ignore --> |
| 20 | <div class="slides"> |
| 21 | |
| 22 | <section> |
| 23 | <h2>reveal.js Math Plugin</h2> |
| 24 | <p>Render math with KaTeX, MathJax 2, MathJax 3 or MathJax 4</p> |
| 25 | </section> |
| 26 | |
| 27 | <section> |
| 28 | <h3>The Lorenz Equations</h3> |
| 29 | |
| 30 | <!-- prettier-ignore --> |
| 31 | \[\begin{aligned} |
| 32 | \dot{x} & = \sigma(y-x) \\ |
| 33 | \dot{y} & = \rho x - y - xz \\ |
| 34 | \dot{z} & = -\beta z + xy |
| 35 | \end{aligned} \] |
| 36 | </section> |
| 37 | |
| 38 | <section> |
| 39 | <h3>The Cauchy-Schwarz Inequality</h3> |
| 40 | |
| 41 | <script type="math/tex; mode=display"> |
| 42 | \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) |
| 43 | </script> |
| 44 | </section> |
| 45 | |
| 46 | <section> |
| 47 | <h3>A Cross Product Formula</h3> |
| 48 | |
| 49 | \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} |
| 50 | \mathbf{i} & \mathbf{j} & \mathbf{k} \\ |
| 51 | \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ |
| 52 | \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 |
| 53 | \end{vmatrix} \] |
| 54 | </section> |
| 55 | |
| 56 | <section> |
| 57 | <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3> |
| 58 | |
| 59 | \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] |
| 60 | </section> |
| 61 | |
| 62 | <section> |
| 63 | <h3>An Identity of Ramanujan</h3> |
| 64 | |
| 65 | \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = |
| 66 | 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} |
| 67 | {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] |
| 68 | </section> |
| 69 | |
| 70 | <section> |
| 71 | <h3>A Rogers-Ramanujan Identity</h3> |
| 72 | |
| 73 | \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = |
| 74 | \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] |
| 75 | </section> |
| 76 | |
| 77 | <section> |
| 78 | <h3>Maxwell’s Equations</h3> |
| 79 | |
| 80 | \[ \begin{aligned} |
| 81 | \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| 82 | \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ |
| 83 | \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} |
| 84 | \] |
| 85 | </section> |
| 86 | |
| 87 | <section> |
| 88 | <h3>TeX Macros</h3> |
| 89 | |
| 90 | Here is a common vector space: |
| 91 | \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\] |
| 92 | used in functional analysis. |
| 93 | </section> |
| 94 | |
| 95 | <section> |
| 96 | <section> |
| 97 | <h3>The Lorenz Equations</h3> |
| 98 | |
| 99 | <div class="fragment"> |
| 100 | \[\begin{aligned} |
| 101 | \dot{x} & = \sigma(y-x) \\ |
| 102 | \dot{y} & = \rho x - y - xz \\ |
| 103 | \dot{z} & = -\beta z + xy |
| 104 | \end{aligned} \] |
| 105 | </div> |
| 106 | </section> |
| 107 | |
| 108 | <section> |
| 109 | <h3>The Cauchy-Schwarz Inequality</h3> |
| 110 | |
| 111 | <div class="fragment"> |
| 112 | \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \] |
| 113 | </div> |
| 114 | </section> |
| 115 | |
| 116 | <section> |
| 117 | <h3>A Cross Product Formula</h3> |
| 118 | |
| 119 | <div class="fragment"> |
| 120 | \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} |
| 121 | \mathbf{i} & \mathbf{j} & \mathbf{k} \\ |
| 122 | \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ |
| 123 | \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 |
| 124 | \end{vmatrix} \] |
| 125 | </div> |
| 126 | </section> |
| 127 | |
| 128 | <section> |
| 129 | <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3> |
| 130 | |
| 131 | <div class="fragment"> |
| 132 | \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \] |
| 133 | </div> |
| 134 | </section> |
| 135 | |
| 136 | <section> |
| 137 | <h3>An Identity of Ramanujan</h3> |
| 138 | |
| 139 | <div class="fragment"> |
| 140 | \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = |
| 141 | 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} |
| 142 | {1+\frac{e^{-8\pi}} {1+\ldots} } } } \] |
| 143 | </div> |
| 144 | </section> |
| 145 | |
| 146 | <section> |
| 147 | <h3>A Rogers-Ramanujan Identity</h3> |
| 148 | |
| 149 | <div class="fragment"> |
| 150 | \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = |
| 151 | \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\] |
| 152 | </div> |
| 153 | </section> |
| 154 | |
| 155 | <section> |
| 156 | <h3>Maxwell’s Equations</h3> |
| 157 | |
| 158 | <div class="fragment"> |
| 159 | \[ \begin{aligned} |
| 160 | \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| 161 | \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ |
| 162 | \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} |
| 163 | \] |
| 164 | </div> |
| 165 | </section> |
| 166 | |
| 167 | <section> |
| 168 | <h3>TeX Macros</h3> |
| 169 | |
| 170 | Here is a common vector space: |
| 171 | \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\] |
| 172 | used in functional analysis. |
| 173 | </section> |
| 174 | |
| 175 | </section> |
| 176 | |
| 177 | </div> |
| 178 | </div> |
| 179 | |
| 180 | <script src="../dist/reveal.js"></script> |
| 181 | <script src="../dist/plugin/math.js"></script> |
| 182 | <script> |
| 183 | Reveal.initialize({ |
| 184 | history: true, |
| 185 | transition: 'linear', |
| 186 | |
| 187 | // MathJax2 configuration (commented out) |
| 188 | /* |
| 189 | mathjax2: { |
| 190 | config: 'TeX-AMS_HTML-full', |
| 191 | TeX: { |
| 192 | Macros: { |
| 193 | R: '\\mathbb{R}', |
| 194 | set: ['\\left\\{#1 \\; ; \\; #2\\right\\}', 2], |
| 195 | }, |
| 196 | }, |
| 197 | }, |
| 198 | */ |
| 199 | |
| 200 | // MathJax4 configuration |
| 201 | mathjax4: { |
| 202 | tex: { |
| 203 | inlineMath: [['$', '$'], ['\\(', '\\)']], |
| 204 | displayMath: [['$$', '$$'], ['\\[', '\\]']], |
| 205 | macros: { |
| 206 | R: '\\mathbb{R}', |
| 207 | set: ['\\left\\{#1 \\; ; \\; #2\\right\\}', 2] |
| 208 | } |
| 209 | }, |
| 210 | options: { |
| 211 | skipHtmlTags: ['script', 'noscript', 'style', 'textarea', 'pre', 'code'] |
| 212 | }, |
| 213 | output: { |
| 214 | font: 'mathjax-stix2', |
| 215 | displayOverflow: 'linebreak', |
| 216 | linebreaks: { // options for when overflow is linebreak |
| 217 | inline: true, // true for browser-based breaking of inline equations |
| 218 | width: '100%', // a fixed size or a percentage of the container width |
| 219 | lineleading: .2, // the default lineleading in em units |
| 220 | LinebreakVisitor: null // The LinebreakVisitor to use |
| 221 | } |
| 222 | } |
| 223 | }, |
| 224 | |
| 225 | // There are four typesetters available |
| 226 | // RevealMath.MathJax2 (default) |
| 227 | // RevealMath.MathJax3 |
| 228 | // RevealMath.MathJax4 |
| 229 | // RevealMath.KaTeX |
| 230 | // |
| 231 | // This example uses MathJax4 with macros support |
| 232 | // More info at https://revealjs.com/math/ |
| 233 | plugins: [ RevealMath.MathJax4 ] |
| 234 | }); |
| 235 | </script> |
| 236 | </body> |
| 237 | </html> |
| 238 |