203 lines
6.4 KiB
HTML
203 lines
6.4 KiB
HTML
<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="utf-8" />
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<title>reveal.js - Math Plugin</title>
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<meta
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name="viewport"
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content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no"
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/>
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<link rel="stylesheet" href="../dist/reveal.css" />
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<link rel="stylesheet" href="../dist/theme/night.css" id="theme" />
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</head>
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<body>
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<div class="reveal">
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<div class="slides">
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<section>
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<h2>reveal.js Math Plugin</h2>
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<p>Render math with KaTeX, MathJax 2 or MathJax 3</p>
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</section>
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<section>
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<h3>The Lorenz Equations</h3>
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\[\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho
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x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} \]
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</section>
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<section>
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<h3>The Cauchy-Schwarz Inequality</h3>
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<script type="math/tex; mode=display">
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\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)
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</script>
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</section>
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<section>
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<h3>A Cross Product Formula</h3>
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\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} &
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\mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} &
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\frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v}
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& \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]
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</section>
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<section>
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<h3>
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The probability of getting \(k\) heads when flipping \(n\) coins is
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</h3>
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\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
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</section>
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<section>
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<h3>An Identity of Ramanujan</h3>
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\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
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1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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</section>
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<section>
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<h3>A Rogers-Ramanujan Identity</h3>
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\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
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</section>
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<section>
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<h3>Maxwell’s Equations</h3>
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\[ \begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\,
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\frac{\partial\vec{\mathbf{E}}}{\partial t} & =
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\frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &
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= 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\,
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\frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}}
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\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} \]
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</section>
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<section>
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<h3>TeX Macros</h3>
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Here is a common vector space: \[L^2(\R) = \set{u : \R \to \R}{\int_\R
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|u|^2 < +\infty}\] used in functional analysis.
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</section>
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<section>
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<section>
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<h3>The Lorenz Equations</h3>
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<div class="fragment">
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\[\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & =
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\rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} \]
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</div>
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</section>
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<section>
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<h3>The Cauchy-Schwarz Inequality</h3>
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<div class="fragment">
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\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n
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a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
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</div>
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</section>
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<section>
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<h3>A Cross Product Formula</h3>
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<div class="fragment">
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\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i}
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& \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u}
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& \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial
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X}{\partial v} & \frac{\partial Y}{\partial v} & 0
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\end{vmatrix} \]
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</div>
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</section>
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<section>
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<h3>
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The probability of getting \(k\) heads when flipping \(n\) coins
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is
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</h3>
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<div class="fragment">
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\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
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</div>
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</section>
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<section>
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<h3>An Identity of Ramanujan</h3>
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<div class="fragment">
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\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}}
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= 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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</div>
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</section>
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<section>
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<h3>A Rogers-Ramanujan Identity</h3>
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<div class="fragment">
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\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
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</div>
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</section>
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<section>
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<h3>Maxwell’s Equations</h3>
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<div class="fragment">
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\[ \begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\,
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\frac{\partial\vec{\mathbf{E}}}{\partial t} & =
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\frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}}
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& = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\,
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\frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & =
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\vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0
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\end{aligned} \]
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</div>
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</section>
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<section>
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<h3>TeX Macros</h3>
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Here is a common vector space: \[L^2(\R) = \set{u : \R \to
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\R}{\int_\R |u|^2 < +\infty}\] used in functional analysis.
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</section>
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</section>
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</div>
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</div>
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<script src="../dist/reveal.js"></script>
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<script src="../plugin/math/math.js"></script>
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<script>
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Reveal.initialize({
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history: true,
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transition: "linear",
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mathjax2: {
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config: "TeX-AMS_HTML-full",
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TeX: {
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Macros: {
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R: "\\mathbb{R}",
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set: ["\\left\\{#1 \\; ; \\; #2\\right\\}", 2],
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},
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},
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},
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// There are three typesetters available
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// RevealMath.MathJax2 (default)
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// RevealMath.MathJax3
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// RevealMath.KaTeX
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//
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// More info at https://revealjs.com/math/
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plugins: [RevealMath.MathJax2],
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});
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</script>
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</body>
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</html>
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