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133 lines
5.8 KiB
133 lines
5.8 KiB
<?xml version="1.0" encoding="utf-8" ?> |
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> |
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<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> |
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<head> |
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> |
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<meta name="generator" content="Docutils 0.14: http://docutils.sourceforge.net/" /> |
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<title>Mathematics</title> |
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<script type="text/javascript" src="/usr/share/javascript/mathjax/MathJax.js?config=TeX-AMS_CHTML"></script> |
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<link rel="stylesheet" href="../input/data/html4css1.css" type="text/css" /> |
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</head> |
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<body> |
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<div class="document" id="mathematics"> |
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<h1 class="title">Mathematics</h1> |
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|
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<p>Docutils supports inline math with the prefix or postfix <tt class="docutils literal">:math:</tt> |
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role specificator, <span class="math">\(n! + \sin(x_n^2)\)</span> and <span class="math">\(A_\text{c} = |
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\frac{\pi}{4} d^2\)</span>, as well as displayed math via the |
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<cite>math</cite> directive:</p> |
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<div class="math"> |
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\begin{equation*} |
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f(\epsilon) = \frac{1}{1 + \exp\left(\frac{\varepsilon}{k_\text{B}T}\right)} |
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\end{equation*} |
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</div> |
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<p>Content may start on the first line of the directive, e.g.</p> |
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<div class="math"> |
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\begin{equation*} |
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N = \frac{\text{number of apples}}{7} |
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\end{equation*} |
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</div> |
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<p>Equations can be labeled with a reference name using the <tt class="docutils literal">:name:</tt> option. |
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See <a class="reference internal" href="#eq-m">eq:M</a> and <a class="reference internal" href="#eq-schrodinger">eq:schrödinger</a> below.</p> |
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<p>The determinant of the matrix</p> |
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<div class="math" id="eq-m"> |
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\begin{equation*} |
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\mathbf{M} = \left(\begin{matrix}a&b\\c&d\end{matrix}\right) |
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\end{equation*} |
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</div> |
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<p>is <span class="math">\(|\mathbf{M}| = ad - bc\)</span>.</p> |
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<p>More than one display math block can be put in one math directive. |
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For example, the following sum and integral with limits:</p> |
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<div class="math"> |
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\begin{equation*} |
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\int_0^1 x^n dx = \frac{1}{n + 1} |
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\end{equation*} |
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</div> |
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<div class="math"> |
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\begin{equation*} |
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\sum_{n=1}^m n = \frac{m(m+1)}{2} |
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\end{equation*} |
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</div> |
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<p>LaTeX-supported Unicode math symbols can be used in math roles and |
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directives:</p> |
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<p>The Schrödinger equation</p> |
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<div class="math" id="eq-schrodinger"> |
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\begin{equation*} |
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i\hbar \frac{\partial }{\partial t}\Psi = \hat{H}\Psi , |
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\end{equation*} |
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</div> |
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<p>with the <em>wave function</em> <span class="math">\(\Psi \)</span>, describes how the quantum state of a |
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physical system changes in time.</p> |
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<dl class="docutils"> |
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<dt>Math-Accents:</dt> |
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<dd><table border="1" class="colwidths-given borderless first last docutils"> |
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<colgroup> |
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<col width="33%" /> |
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<col width="33%" /> |
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<col width="33%" /> |
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</colgroup> |
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<tbody valign="top"> |
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<tr><td><span class="math">\(\acute{a}\)</span> <tt class="docutils literal">\acute{a}</tt></td> |
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<td><span class="math">\(\dot{t}\)</span> <tt class="docutils literal">\dot{t}</tt></td> |
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<td><span class="math">\(\hat{\gamma}\)</span> <tt class="docutils literal"><span class="pre">\hat{\gamma}</span></tt></td> |
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</tr> |
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<tr><td><span class="math">\(\grave{a}\)</span> <tt class="docutils literal">\grave{a}</tt></td> |
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<td><span class="math">\(\ddot{t}\)</span> <tt class="docutils literal">\ddot{t}</tt></td> |
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<td><span class="math">\(\tilde{\alpha}\)</span> <tt class="docutils literal"><span class="pre">\tilde{\alpha}</span></tt></td> |
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</tr> |
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<tr><td><span class="math">\(\breve{x}\)</span> <tt class="docutils literal">\breve{x}</tt></td> |
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<td><span class="math">\(\dddot{t}\)</span> <tt class="docutils literal">\dddot{t}</tt></td> |
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<td><span class="math">\(\vec{\imath}\)</span> <tt class="docutils literal"><span class="pre">\vec{\imath}</span></tt></td> |
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</tr> |
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<tr><td><span class="math">\(\check{a}\)</span> <tt class="docutils literal">\check{a}</tt></td> |
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<td><span class="math">\(\bar{a}\)</span> <tt class="docutils literal">\bar{a}</tt></td> |
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<td><span class="math">\(\vec{R}\)</span> <tt class="docutils literal">\vec{R}</tt></td> |
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</tr> |
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</tbody> |
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</table> |
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</dd> |
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</dl> |
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<!-- \widetilde{xxx} |
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\widehat{xxx} --> |
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<p>Modulation Transfer Function:</p> |
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<div class="math"> |
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\begin{equation*} |
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\text{MTF} = \left|\frac{\mathcal{F}\{s(x)\}} |
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{\mathcal{F}\{ s(x)\} |_{\omega _{x}=0}}\right| |
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= \mathrm{abs}\left(\frac |
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{\int _{-\infty }^{\infty }s(x) \mathrm{e}^{\mathrm{i}\omega _{x}x}\mathrm{d}{x}} |
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{\int _{-\infty }^{\infty }s(x)\mathrm{d}{x}} |
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\right). |
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\end{equation*} |
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</div> |
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<p>Math split over two lines: If a double backslash is detected outside a |
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<tt class="docutils literal"><span class="pre">\begin{...}</span> <span class="pre">\end{...}</span></tt> pair, the math code is wrapped in an <a class="reference external" href="ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath</a> |
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<tt class="docutils literal">align</tt> environment:</p> |
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<div class="math"> |
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\begin{align*} |
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s_{\mathrm{out}}(x) & = s_{\mathrm{in}}(x') * s_\delta (x-x') \\ |
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& = \int s_{\mathrm{in}}(x')s_\delta (x-x')\mathrm{d}x' |
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\end{align*} |
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</div> |
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<p>Cases ("manually", with <tt class="docutils literal">matrix</tt> environment):</p> |
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<div class="math"> |
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\begin{equation*} |
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\mathrm{sgn}(x) = \left\{\begin{matrix} |
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-1 & x<0\\ |
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1 & x>0 |
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\end{matrix}\right. |
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\end{equation*} |
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</div> |
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<p>Cases with the <a class="reference external" href="ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath</a> <tt class="docutils literal">cases</tt> environment (not (yet) supported by |
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HTML writers with <tt class="docutils literal"><span class="pre">--math-output=MathML</span></tt>):</p> |
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<div class="math"> |
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\begin{equation*} |
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\mathrm{sgn}(x) = \begin{cases} |
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-1 & x<0\\ |
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1 & x>0 |
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\end{cases} |
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\end{equation*} |
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</div> |
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</div> |
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</body> |
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</html>
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