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Ajout de formatage pour slides et précisions

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François Pelletier 2023-11-27 00:15:21 -05:00
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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>
\[\begin{aligned}
\dot{x} &amp; = \sigma(y-x) \\
\dot{y} &amp; = \rho x - y - xz \\
\dot{z} &amp; = -\beta z + xy
\end{aligned} \]
</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>
<h3>TeX Macros</h3>
Here is a common vector space:
\[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
used in functional analysis.
</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>
<h3>TeX Macros</h3>
Here is a common vector space:
\[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
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>