208 lines
5.6 KiB
HTML
208 lines
5.6 KiB
HTML
<!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>
|
|
<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="../../lib/js/head.min.js"></script>
|
|
<script src="../../js/reveal.js"></script>
|
|
|
|
<script>
|
|
|
|
Reveal.initialize({
|
|
history: true,
|
|
transition: 'linear',
|
|
|
|
math: {
|
|
// mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
|
|
config: 'TeX-AMS_HTML-full',
|
|
TeX: {
|
|
Macros: {
|
|
R: '\\mathbb{R}',
|
|
set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ]
|
|
}
|
|
}
|
|
},
|
|
|
|
dependencies: [
|
|
{ src: '../../lib/js/classList.js' },
|
|
{ src: '../../plugin/math/math.js', async: true }
|
|
]
|
|
});
|
|
|
|
</script>
|
|
|
|
</body>
|
|
</html>
|