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diff --git a/static/presentations/2021-11-13/garage/examples/math.html b/static/presentations/2021-11-13/garage/examples/math.html new file mode 100644 index 0000000..bd2e75a --- /dev/null +++ b/static/presentations/2021-11-13/garage/examples/math.html @@ -0,0 +1,206 @@ +<!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="../dist/reveal.css"> + <link rel="stylesheet" href="../dist/theme/night.css" id="theme"> + </head> + + <body> + + <div class="reveal"> + + <div class="slides"> + + <section> + <h2>reveal.js Math Plugin</h2> + <p>Render math with KaTeX, MathJax 2 or MathJax 3</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> + <h3>TeX Macros</h3> + + Here is a common vector space: + \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\] + used in functional analysis. + </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> + <h3>TeX Macros</h3> + + Here is a common vector space: + \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 < +\infty}\] + used in functional analysis. + </section> + </section> + + </div> + + </div> + + <script src="../dist/reveal.js"></script> + <script src="../plugin/math/math.js"></script> + <script> + Reveal.initialize({ + history: true, + transition: 'linear', + + mathjax2: { + config: 'TeX-AMS_HTML-full', + TeX: { + Macros: { + R: '\\mathbb{R}', + set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ] + } + } + }, + + // There are three typesetters available + // RevealMath.MathJax2 (default) + // RevealMath.MathJax3 + // RevealMath.KaTeX + // + // More info at https://revealjs.com/math/ + plugins: [ RevealMath.MathJax2 ] + }); + </script> + + </body> +</html> |