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-<!doctype html>
-<html lang="en">
-
- <head>
- <meta charset="utf-8">
-
- <title>reveal.js - Math Plugin</title>
-
- <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
-
- <link rel="stylesheet" href="../../css/reveal.css">
- <link rel="stylesheet" href="../../css/theme/night.css" id="theme">
- </head>
-
- <body>
-
- <div class="reveal">
-
- <div class="slides">
-
- <section>
- <h2>reveal.js Math Plugin</h2>
- <p>A thin wrapper for MathJax</p>
- </section>
-
- <section>
- <h3>The Lorenz Equations</h3>
-
- \[\begin{aligned}
- \dot{x} &amp; = \sigma(y-x) \\
- \dot{y} &amp; = \rho x - y - xz \\
- \dot{z} &amp; = -\beta z + xy
- \end{aligned} \]
- </section>
-
- <section>
- <h3>The Cauchy-Schwarz Inequality</h3>
-
- <script type="math/tex; mode=display">
- \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)
- </script>
- </section>
-
- <section>
- <h3>A Cross Product Formula</h3>
-
- \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
- \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
- \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
- \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
- \end{vmatrix} \]
- </section>
-
- <section>
- <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
-
- \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
- </section>
-
- <section>
- <h3>An Identity of Ramanujan</h3>
-
- \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
- 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
- {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
- </section>
-
- <section>
- <h3>A Rogers-Ramanujan Identity</h3>
-
- \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
- \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
- </section>
-
- <section>
- <h3>Maxwell&#8217;s Equations</h3>
-
- \[ \begin{aligned}
- \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
- \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
- \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
- \]
- </section>
-
- <section>
- <section>
- <h3>The Lorenz Equations</h3>
-
- <div class="fragment">
- \[\begin{aligned}
- \dot{x} &amp; = \sigma(y-x) \\
- \dot{y} &amp; = \rho x - y - xz \\
- \dot{z} &amp; = -\beta z + xy
- \end{aligned} \]
- </div>
- </section>
-
- <section>
- <h3>The Cauchy-Schwarz Inequality</h3>
-
- <div class="fragment">
- \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
- </div>
- </section>
-
- <section>
- <h3>A Cross Product Formula</h3>
-
- <div class="fragment">
- \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
- \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
- \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
- \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
- \end{vmatrix} \]
- </div>
- </section>
-
- <section>
- <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
-
- <div class="fragment">
- \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
- </div>
- </section>
-
- <section>
- <h3>An Identity of Ramanujan</h3>
-
- <div class="fragment">
- \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
- 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
- {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
- </div>
- </section>
-
- <section>
- <h3>A Rogers-Ramanujan Identity</h3>
-
- <div class="fragment">
- \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
- \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
- </div>
- </section>
-
- <section>
- <h3>Maxwell&#8217;s Equations</h3>
-
- <div class="fragment">
- \[ \begin{aligned}
- \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
- \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
- \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
- \]
- </div>
- </section>
- </section>
-
- </div>
-
- </div>
-
- <script src="../../lib/js/head.min.js"></script>
- <script src="../../js/reveal.js"></script>
-
- <script>
-
- Reveal.initialize({
- history: true,
- transition: 'linear',
-
- math: {
- // mathjax: 'http://cdn.mathjax.org/mathjax/latest/MathJax.js',
- config: 'TeX-AMS_HTML-full'
- },
-
- dependencies: [
- { src: '../../lib/js/classList.js' },
- { src: '../../plugin/math/math.js', async: true }
- ]
- });
-
- </script>
-
- </body>
-</html>