docs/com/test/examples/math.html

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   7                 <title>reveal.js - Math Plugin</title>
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  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                                         \[\begin{aligned}
  30                                         \dot{x} &amp; = \sigma(y-x) \\
  31                                         \dot{y} &amp; = \rho x - y - xz \\
  32                                         \dot{z} &amp; = -\beta z + xy
  33                                         \end{aligned} \]
  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                                         \[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
  48                                         \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
  49                                         \frac{\partial X}{\partial u} &amp;  \frac{\partial Y}{\partial u} &amp; 0 \\
  50                                         \frac{\partial X}{\partial v} &amp;  \frac{\partial Y}{\partial v} &amp; 0
  51                                         \end{vmatrix}  \]
  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&#8217;s Equations</h3>
  77
  78                                         \[  \begin{aligned}
  79                                         \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
  80                                         \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
  81                                         \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
  82                                         \]
  83                                 </section>
  84
  85                                 <section>
  86                                         <section>
  87                                                 <h3>The Lorenz Equations</h3>
  88
  89                                                 <div class="fragment">
  90                                                         \[\begin{aligned}
  91                                                         \dot{x} &amp; = \sigma(y-x) \\
  92                                                         \dot{y} &amp; = \rho x - y - xz \\
  93                                                         \dot{z} &amp; = -\beta z + xy
  94                                                         \end{aligned} \]
  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                                                         \[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
 111                                                         \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
 112                                                         \frac{\partial X}{\partial u} &amp;  \frac{\partial Y}{\partial u} &amp; 0 \\
 113                                                         \frac{\partial X}{\partial v} &amp;  \frac{\partial Y}{\partial v} &amp; 0
 114                                                         \end{vmatrix}  \]
 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&#8217;s Equations</h3>
 147
 148                                                 <div class="fragment">
 149                                                         \[  \begin{aligned}
 150                                                         \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\   \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
 151                                                         \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
 152                                                         \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
 153                                                         \]
 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>