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e2243bf7a9
version 3 is more performant, smaller and simpler to integrate, without monkeypatching. On the down side, it does not do line breaking, as yet. Note that only the viewer is currently ported
103 lines
2.8 KiB
HTML
103 lines
2.8 KiB
HTML
<!DOCTYPE html>
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<html>
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<!-- Copyright (c) 2012 Design Science, Inc. -->
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<head>
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<title>Math Test Page</title>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
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<!-- This script tag is needed to make calibre's ebook-viewer recpgnize that this file needs math typesetting -->
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<script type="text/x-mathjax-config">
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// This line adds numbers to all equations automatically, unless explicitly suppressed.
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MathJax.tex = {tags: 'all'};
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</script>
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<style>
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h1 {text-align:center}
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h2 {
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font-weight: bold;
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background-color: #DDDDDD;
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padding: .2em .5em;
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margin-top: 1.5em;
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border-top: 3px solid #666666;
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border-bottom: 2px solid #999999;
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}
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</style>
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</head>
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<body>
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<h1>Sample Equations</h1>
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<h2>The Lorenz Equations</h2>
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<p>
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\begin{align}
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\dot{x} & = \sigma(y-x) \label{lorenz}\\
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\dot{y} & = \rho x - y - xz \\
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\dot{z} & = -\beta z + xy
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\end{align}
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</p>
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<h2>The Cauchy-Schwarz Inequality</h2>
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<p>\[
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\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq
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\left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
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\]</p>
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<h2>A Cross Product Formula</h2>
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<p>\[
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\mathbf{V}_1 \times \mathbf{V}_2 =
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\begin{vmatrix}
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\mathbf{i} & \mathbf{j} & \mathbf{k} \\
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\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
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\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\
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\end{vmatrix}
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\]</p>
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<h2>The probability of getting \(k\) heads when flipping \(n\) coins is:</h2>
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<p>\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]</p>
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<h2>An Identity of Ramanujan</h2>
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<p>\[
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\frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =
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1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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{1+\frac{e^{-8\pi}} {1+\ldots} } } }
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\]</p>
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<h2>A Rogers-Ramanujan Identity</h2>
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<p>\[
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1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
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\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
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\quad\quad \text{for $|q|<1$}.
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\]</p>
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<h2>Maxwell's Equations</h2>
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<p>
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\begin{align}
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\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\
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\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
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\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
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\nabla \cdot \vec{\mathbf{B}} & = 0
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\end{align}
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</p>
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<h2>In-line Mathematics</h2>
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<p>While display equations look good for a page of samples, the
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ability to mix math and text in a paragraph is also important. This
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expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. As
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you see, equations can be used this way as well, without unduly
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disturbing the spacing between lines.</p>
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<h2>References to equations</h2>
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<p>Here is a reference to the Lorenz Equations (\ref{lorenz}). Clicking on the equation number will take you back to the equation.</p>
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</body>
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</html>
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