| <!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> |
| |
| \[\begin{aligned} |
| \dot{x} & = \sigma(y-x) \\ |
| \dot{y} & = \rho x - y - xz \\ |
| \dot{z} & = -\beta z + xy |
| \end{aligned} \] |
| </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> |
| |
| \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} |
| \mathbf{i} & \mathbf{j} & \mathbf{k} \\ |
| \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ |
| \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 |
| \end{vmatrix} \] |
| </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’s Equations</h3> |
| |
| \[ \begin{aligned} |
| \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ |
| \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} |
| \] |
| </section> |
| |
| <section> |
| <section> |
| <h3>The Lorenz Equations</h3> |
| |
| <div class="fragment"> |
| \[\begin{aligned} |
| \dot{x} & = \sigma(y-x) \\ |
| \dot{y} & = \rho x - y - xz \\ |
| \dot{z} & = -\beta z + xy |
| \end{aligned} \] |
| </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"> |
| \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} |
| \mathbf{i} & \mathbf{j} & \mathbf{k} \\ |
| \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ |
| \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 |
| \end{vmatrix} \] |
| </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’s Equations</h3> |
| |
| <div class="fragment"> |
| \[ \begin{aligned} |
| \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ |
| \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ |
| \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} |
| \] |
| </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> |