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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<HTML xmlns="http://www.w3.org/1999/xhtml" dir="ltr" lang="en-US" xml:lang="en-US">
<HEAD>
<TITLE>MathJax Test Page</TITLE>
<!-- Copyright (c) 2009 Design Science, Inc. -->
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=UTF-8" />
<META HTTP-EQUIV="X-UA-Compatible" CONTENT="IE=EmulateIE7" >
<SCRIPT SRC="../MathJax.js">
MathJax.Hub.Config({
extensions: ["tex2jax.js"],
jax: ["input/TeX","output/HTML-CSS"],
tex2jax: {inlineMath: [["$","$"],["\\(","\\)"]]}
});
</SCRIPT>
</HEAD>
<BODY>
<NOSCRIPT>
<DIV STYLE="color:#CC0000; text-align:center">
<B>Warning: <A HREF="http://www.mathjax.org/">MathJax</A>
requires JavaScript to process the mathematics on this page.<BR>
If your browser supports JavaScript, be sure it is enabled.<B>
</DIV>
<HR>
</NOSCRIPT>
<BLOCKQUOTE>
<p><b>The Lorenz Equations</b></p>
<p>
\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}
</p>
<p><b>The Cauchy-Schwarz Inequality</b></p>
<p>\[
\left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq
\left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\]</p>
<p><b>A Cross Product Formula</b></p>
<p>\[
\mathbf{V}_1 \times \mathbf{V}_2 =
\begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\
\end{vmatrix}
\]</p>
<p><b>The probability of getting \(k\) heads when flipping \(n\) coins is:</b></p>
<p>\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]</p>
<p><b>An Identity of Ramanujan</b></p>
<p>\[
\frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }
\]</p>
<p><b>A Rogers-Ramanujan Identity</b></p>
<p>\[
1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}.
\]</p>
<p><b>Maxwell's Equations</b></p>
<p>
\begin{align}
\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{align}
</p>
<p>Finally, while display equations look good for a page of samples, the
ability to mix math and text in a paragraph is also important. This
expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. As
you see, MathJax equations can be used this way as well, without unduly
disturbing the spacing between lines.</p>
</BLOCKQUOTE>
</BODY>
</HTML>
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