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examples/math.html
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hakimel
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12 ноя 2021, 12:48
12 ноя 2021, 12:48
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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="../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>