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<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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