<!DOCTYPE html> <html> <head> <title>MathJax Test Page</title> <!– Copyright © 2009-2018 The MathJax Consortium –> <meta http-equiv=“Content-Type” content=“text/html; charset=UTF-8” /> <meta http-equiv=“X-UA-Compatible” content=“IE=edge” /> <meta name=“viewport” content=“width=device-width, initial-scale=1”>

<script type=“text/x-mathjax-config”>

MathJax.Hub.Config({
  extensions: ["tex2jax.js"],
  jax: ["input/TeX","output/HTML-CSS"],
  tex2jax: {inlineMath: [["$","$"],["\\(","\\)"]]}
});

</script> <script type=“text/javascript” src=“../MathJax.js”></script>

<style> h1 {text-align:center} h2 {

font-weight: bold;
background-color: #DDDDDD;
padding: .2em .5em;
margin-top: 1.5em;
border-top: 3px solid #666666;
border-bottom: 2px solid #999999;

} </style> </head> <body>

<noscript> <div style=“color:#CC0000; text-align:center”> 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. </div> <hr> </noscript>

<h1>Sample MathJax Equations</h1>

<blockquote>

<h2>The Lorenz Equations</h2>

<p> begin{align} dot{x} & = sigma(y-x) \ dot{y} & = rho x - y - xz \ dot{z} & = -beta z + xy end{align} </p>

<h2>The Cauchy-Schwarz Inequality</h2>

<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>

<h2>A Cross Product Formula</h2>

<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>

<h2>The probability of getting (k) heads when flipping (n) coins is:</h2>

<p>[P(E) = {n choose k} p^k (1-p)^{ n-k} ]</p>

<h2>An Identity of Ramanujan</h2>

<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>

<h2>A Rogers-Ramanujan Identity</h2>

<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>

<h2>Maxwell's Equations</h2>

<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>

<h2>In-line Mathematics</h2>

<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>

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