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Typesetting_Equations.html
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<nav class="navbar navbar-default">
<div class="container-fluid">
<ul class="nav navbar-nav">
<li><a href="index.html">Home</a></li>
<li class="dropdown"><a href="#"> Documentation </a>
<div class="dropdown-content">
<a href="Notebook_Server_on_Palmetto.html"> Requesting a Notebook Server </a>
<a href="Jupyter_Interface.html"> Interface </a>
<a href="Quick_Start.html"> Notebook Quick Start </a>
<a href="Notebook_Basics.html"> Notebook Basics </a>
<a href="Working_With_Markdown_Cells.html"> Markdown Cells </a>
<a href="Typesetting_Equations.html"> Typesetting Equations </a>
<a href="Configuring.html"> Customizing Jupyter </a>
<a href="Sharing_Notebooks.html"> Sharing Notebooks </a>
</div>
</li>
<li><a href="troubleshooting.html"> Troubleshooting/FAQ </a></li>
<li><a href="resources.html"> Resources </a></li>
<li><a href="help.html"> Getting Help </a></li>
</ul>
</div>
</nav>
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<title>Typesetting_Equations</title>
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<p>The Markdown parser included in the Jupyter Notebook is MathJax-aware. This means that you can freely mix in mathematical expressions using the <a href="http://docs.mathjax.org/en/latest/tex.html#tex-support">MathJax subset of Tex and LaTeX</a>. <a href="http://www.mathjax.org/demos/tex-samples/">Some examples from the MathJax site</a> are reproduced below, as well as the Markdown+TeX source.</p>
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<h1 id="Motivating-Examples">Motivating Examples<a class="anchor-link" href="#Motivating-Examples">¶</a></h1><h2 id="The-Lorenz-Equations">The Lorenz Equations<a class="anchor-link" href="#The-Lorenz-Equations">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><p>$\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}$</p>
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<h2 id="The-Cauchy-Schwarz-Inequality">The Cauchy-Schwarz Inequality<a class="anchor-link" href="#The-Cauchy-Schwarz-Inequality">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\begin{equation*}
\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)
\end{equation*}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><p>$\begin{equation*}
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
\end{equation*}$</p>
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<h2 id="A-Cross-Product-Formula">A Cross Product Formula<a class="anchor-link" href="#A-Cross-Product-Formula">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\begin{equation*}
\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}
\end{equation*}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><p>$\begin{equation*}
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{vmatrix}
\end{equation*}$</p>
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<h2 id="The-probability-of-getting-(k)-heads-when-flipping-(n)-coins-is">The probability of getting (k) heads when flipping (n) coins is<a class="anchor-link" href="#The-probability-of-getting-(k)-heads-when-flipping-(n)-coins-is">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\begin{equation*}
P(E) = {n \choose k} p^k (1-p)^{ n-k}
\end{equation*}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><p>$\begin{equation*}
P(E) = {n \choose k} p^k (1-p)^{ n-k}
\end{equation*}$</p>
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<h2 id="An-Identity-of-Ramanujan">An Identity of Ramanujan<a class="anchor-link" href="#An-Identity-of-Ramanujan">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\begin{equation*}
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) 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} } } }
\end{equation*}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><p>$\begin{equation*}
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }
\end{equation*}$</p>
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<h2 id="A-Rogers-Ramanujan-Identity">A Rogers-Ramanujan Identity<a class="anchor-link" href="#A-Rogers-Ramanujan-Identity">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\begin{equation*}
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 $|q|<1$}.
\end{equation*}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3>$$\begin{equation*}
1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
\quad\quad \text{for $|q|<1$}.
\end{equation*}$$
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<h2 id="Maxwell's-Equations">Maxwell's Equations<a class="anchor-link" href="#Maxwell's-Equations">¶</a></h2><h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>\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}</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><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>
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<h2 id="Equation-Numbering-and-References">Equation Numbering and References<a class="anchor-link" href="#Equation-Numbering-and-References">¶</a></h2><p>Equation numbering and referencing will be available in a future version of the Jupyter notebook.</p>
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<h2 id="Inline-Typesetting-(Mixing-Markdown-and-TeX)">Inline Typesetting (Mixing Markdown and TeX)<a class="anchor-link" href="#Inline-Typesetting-(Mixing-Markdown-and-TeX)">¶</a></h2><p>While display equations look good for a page of samples, the ability to mix math and <em>formatted</em> <strong>text</strong> in a paragraph is also important.</p>
<h3 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h3>
<pre><code>This expression $\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a [Markdown-formatted](http://daringfireball.net/projects/markdown/) sentence.</code></pre>
<h3 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h3><p>This expression $\sqrt{3x-1}+(1+x)^2$ is an example of a TeX inline equation in a <a href="http://daringfireball.net/projects/markdown/">Markdown-formatted</a> sentence.</p>
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<h2 id="Other-Syntax">Other Syntax<a class="anchor-link" href="#Other-Syntax">¶</a></h2><p>You will notice in other places on the web that <code>$$</code> are needed explicitly to begin and end MathJax typesetting. This is <strong>not</strong> required if you will be using TeX environments, but the Jupyter notebook will accept this syntax on legacy notebooks.</p>
<h2 id="Source">Source<a class="anchor-link" href="#Source">¶</a></h2>
<pre><code>$$
\begin{array}{c}
y_1 \\\
y_2 \mathtt{t}_i \\\
z_{3,4}
\end{array}
$$</code></pre>
<pre><code>$$
\begin{array}{c}
y_1 \cr
y_2 \mathtt{t}_i \cr
y_{3}
\end{array}
$$</code></pre>
<pre><code>$$\begin{eqnarray}
x' &=& &x \sin\phi &+& z \cos\phi \\
z' &=& - &x \cos\phi &+& z \sin\phi \\
\end{eqnarray}$$</code></pre>
<pre><code>$$
x=4
$$</code></pre>
<h2 id="Display">Display<a class="anchor-link" href="#Display">¶</a></h2>$$
\begin{array}{c}
y_1 \\\
y_2 \mathtt{t}_i \\\
z_{3,4}
\end{array}
$$$$
\begin{array}{c}
y_1 \cr
y_2 \mathtt{t}_i \cr
y_{3}
\end{array}
$$$$\begin{eqnarray}
x' &=& &x \sin\phi &+& z \cos\phi \\
z' &=& - &x \cos\phi &+& z \sin\phi \\
\end{eqnarray}$$$$
x=4
$$
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