100 lines
2.8 KiB
HTML
100 lines
2.8 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<HTML xmlns="http://www.w3.org/1999/xhtml" dir="ltr" lang="en-US" xml:lang="en-US">
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<HEAD>
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<TITLE>MathJax Test Page</TITLE>
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<!-- Copyright (c) 2009 Design Science, Inc. -->
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<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=UTF-8" />
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<META HTTP-EQUIV="X-UA-Compatible" CONTENT="IE=EmulateIE7" >
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<SCRIPT SRC="../MathJax.js">
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MathJax.Hub.Config({
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extensions: ["tex2jax.js"],
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jax: ["input/TeX","output/HTML-CSS"],
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tex2jax: {inlineMath: [["$","$"],["\\(","\\)"]]}
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});
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</SCRIPT>
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</HEAD>
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<BODY>
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<NOSCRIPT>
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<DIV STYLE="color:#CC0000; text-align:center">
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<B>Warning: <A HREF="http://www.mathjax.org/">MathJax</A>
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requires JavaScript to process the mathematics on this page.<BR>
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If your browser supports JavaScript, be sure it is enabled.<B>
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</DIV>
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<HR>
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</NOSCRIPT>
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<BLOCKQUOTE>
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<p><b>The Lorenz Equations</b></p>
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<p>
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\begin{align}
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\dot{x} & = \sigma(y-x) \\
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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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<p><b>The Cauchy-Schwarz Inequality</b></p>
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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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<p><b>A Cross Product Formula</b></p>
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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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<p><b>The probability of getting \(k\) heads when flipping \(n\) coins is:</b></p>
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<p>\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]</p>
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<p><b>An Identity of Ramanujan</b></p>
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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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<p><b>A Rogers-Ramanujan Identity</b></p>
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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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<p><b>Maxwell's Equations</b></p>
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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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<p>Finally, 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, MathJax equations can be used this way as well, without unduly
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disturbing the spacing between lines.</p>
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</BLOCKQUOTE>
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</BODY>
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</HTML>
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