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korap.ids-mannheim.de / IDS-Mannheim / revealjs / e1893aed9df79d26db48538ace56cc0d55ae2f0c / . / inst / reveal.js-4.1.2 / examples / math.html
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JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]1<!doctype html>
2<html lang="en">
3
4 <head>
5 <meta charset="utf-8">
6
7 <title>reveal.js - Math Plugin</title>
8
9 <meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
10
Christophe Dervieuxe1893ae2021-10-07 17:09:02 +0200[diff] [blame^]11 <link rel="stylesheet" href="../dist/reveal.css">
12 <link rel="stylesheet" href="../dist/theme/night.css" id="theme">
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]13 </head>
14
15 <body>
16
17 <div class="reveal">
18
19 <div class="slides">
20
21 <section>
22 <h2>reveal.js Math Plugin</h2>
23 <p>A thin wrapper for MathJax</p>
24 </section>
25
26 <section>
27 <h3>The Lorenz Equations</h3>
28
29 \[\begin{aligned}
30 \dot{x} &amp; = \sigma(y-x) \\
31 \dot{y} &amp; = \rho x - y - xz \\
32 \dot{z} &amp; = -\beta z + xy
33 \end{aligned} \]
34 </section>
35
36 <section>
37 <h3>The Cauchy-Schwarz Inequality</h3>
38
39 <script type="math/tex; mode=display">
40 \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)
41 </script>
42 </section>
43
44 <section>
45 <h3>A Cross Product Formula</h3>
46
47 \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
48 \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
49 \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
50 \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
51 \end{vmatrix} \]
52 </section>
53
54 <section>
55 <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
56
57 \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
58 </section>
59
60 <section>
61 <h3>An Identity of Ramanujan</h3>
62
63 \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
64 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
65 {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
66 </section>
67
68 <section>
69 <h3>A Rogers-Ramanujan Identity</h3>
70
71 \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
72 \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
73 </section>
74
75 <section>
76 <h3>Maxwell&#8217;s Equations</h3>
77
78 \[ \begin{aligned}
79 \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
80 \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
81 \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
82 \]
83 </section>
84
85 <section>
Christophe Dervieuxe1893ae2021-10-07 17:09:02 +0200[diff] [blame^]86 <h3>TeX Macros</h3>
87
88 Here is a common vector space:
89 \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
90 used in functional analysis.
91 </section>
92
93 <section>
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]94 <section>
95 <h3>The Lorenz Equations</h3>
96
97 <div class="fragment">
98 \[\begin{aligned}
99 \dot{x} &amp; = \sigma(y-x) \\
100 \dot{y} &amp; = \rho x - y - xz \\
101 \dot{z} &amp; = -\beta z + xy
102 \end{aligned} \]
103 </div>
104 </section>
105
106 <section>
107 <h3>The Cauchy-Schwarz Inequality</h3>
108
109 <div class="fragment">
110 \[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
111 </div>
112 </section>
113
114 <section>
115 <h3>A Cross Product Formula</h3>
116
117 <div class="fragment">
118 \[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
119 \mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
120 \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0 \\
121 \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0
122 \end{vmatrix} \]
123 </div>
124 </section>
125
126 <section>
127 <h3>The probability of getting \(k\) heads when flipping \(n\) coins is</h3>
128
129 <div class="fragment">
130 \[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
131 </div>
132 </section>
133
134 <section>
135 <h3>An Identity of Ramanujan</h3>
136
137 <div class="fragment">
138 \[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
139 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
140 {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
141 </div>
142 </section>
143
144 <section>
145 <h3>A Rogers-Ramanujan Identity</h3>
146
147 <div class="fragment">
148 \[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
149 \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}\]
150 </div>
151 </section>
152
153 <section>
154 <h3>Maxwell&#8217;s Equations</h3>
155
156 <div class="fragment">
157 \[ \begin{aligned}
158 \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\
159 \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\
160 \nabla \cdot \vec{\mathbf{B}} &amp; = 0 \end{aligned}
161 \]
162 </div>
163 </section>
Christophe Dervieuxe1893ae2021-10-07 17:09:02 +0200[diff] [blame^]164
165 <section>
166 <h3>TeX Macros</h3>
167
168 Here is a common vector space:
169 \[L^2(\R) = \set{u : \R \to \R}{\int_\R |u|^2 &lt; +\infty}\]
170 used in functional analysis.
171 </section>
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]172 </section>
173
174 </div>
175
176 </div>
177
Christophe Dervieuxe1893ae2021-10-07 17:09:02 +0200[diff] [blame^]178 <script src="../dist/reveal.js"></script>
179 <script src="../plugin/math/math.js"></script>
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]180 <script>
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]181 Reveal.initialize({
182 history: true,
183 transition: 'linear',
184
185 math: {
Christophe Dervieuxe1893ae2021-10-07 17:09:02 +0200[diff] [blame^]186 // mathjax: 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js',
187 config: 'TeX-AMS_HTML-full',
188 TeX: {
189 Macros: {
190 R: '\\mathbb{R}',
191 set: [ '\\left\\{#1 \\; ; \\; #2\\right\\}', 2 ]
192 }
193 }
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]194 },
195
Christophe Dervieuxe1893ae2021-10-07 17:09:02 +0200[diff] [blame^]196 plugins: [ RevealMath ]
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]197 });
JJ Allaireefa6ad42016-01-30 13:12:05 -0500[diff] [blame]198 </script>
199
200 </body>
201</html>