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97 lines
3.5 KiB
97 lines
3.5 KiB
6 years ago
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<!DOCTYPE html>
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<html lang="en-US">
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<head>
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<meta charset="UTF-8" />
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<meta http-equiv="X-UA-Compatible" content="IE=edge"/>
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<title>MathJax | TeX Samples</title>
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<link rel="stylesheet" type="text/css" media="all" href="http://www.mathjax.org/wp-content/themes/mathjax/style.css" />
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<link rel='stylesheet' id='mt-shcore-style-css' href='http://www.mathjax.org/wp-content/plugins/syntax-highlighter-mt/styles/shCore.css?ver=2.2.4' type='text/css' media='all' />
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<link rel='stylesheet' id='mt-theme-style-css' href='http://www.mathjax.org/wp-content/plugins/syntax-highlighter-mt/styles/shThemeDefault.css?ver=2.2.4' type='text/css' media='all' />
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<style type="text/css" id="custom-background-css">
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body.custom-background { background-color: #d2d3d3; }
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</style>
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</head>
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<body class="page page-id-612 page-child parent-pageid-13 page-template-default custom-background">
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<div id="wrapper" class="hfeed">
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<div id="main">
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<div id="container">
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<div id="content" role="main">
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<div id="post-612" class="post-612 page type-page status-publish hentry">
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<h1 class="entry-title">TeX Samples</h1>
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<div class="entry-content">
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<p>The following equations are represented in the HTML source code as LaTeX expressions.</p>
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<div class="math-header">The Lorenz Equations</div>
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\[\begin{aligned}
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\dot{x} & = \sigma(y-x) \\
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\dot{y} & = \rho x - y - xz \\
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\dot{z} & = -\beta z + xy
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\end{aligned} \]
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<div class="math-header">The Cauchy-Schwarz Inequality</div>
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\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
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<div class="math-header">A Cross Product Formula</div>
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\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
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\mathbf{i} & \mathbf{j} & \mathbf{k} \\
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\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
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\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
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\end{vmatrix} \]
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<div class="math-header">The probability of getting \(k\) heads when flipping \(n\) coins is</div>
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\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
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<div class="math-header">An Identity of Ramanujan</div>
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\[ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
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1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
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{1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
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<div class="math-header">A Rogers-Ramanujan Identity</div>
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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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<div class="math-header">Maxwell’s Equations</div>
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\[ \begin{aligned}
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\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
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\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
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\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
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\]
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<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> </div><!-- .entry-content -->
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</div><!-- #post-## -->
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<div id="comments">
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</div><!-- #comments -->
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</div><!-- #content -->
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</div><!-- #container -->
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<style>#content { margin: 0 0 36px 0; }</style>
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</div><!-- #main -->
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</div><!-- #wrapper -->
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</body>
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</html>
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