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7 <title>Mathematics
</title>
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12 <div class=
"document" id=
"mathematics">
13 <h1 class=
"title">Mathematics
</h1>
15 <p>Docutils supports inline math with the prefix or postfix
<tt class=
"docutils literal">:math:
</tt>
16 role specificator,
<span class=
"math">\(n! + \sin(x_n^
2)\)
</span>
17 and
<span class=
"math">\(A_\text{c} =
18 \frac{\pi}{
4} d^
2\)
</span>
19 , as well as displayed math via the
20 <cite>math
</cite> directive:
</p>
23 f(\epsilon) = \frac{
1}{
1 + \exp\left(\frac{\varepsilon}{k_\text{B}T}\right)}
26 <p>Content may start on the first line of the directive, e.g.
</p>
29 N = \frac{\text{number of apples}}{
7}
32 <p>Equations can be labeled with a reference name using the
<tt class=
"docutils literal">:name:
</tt> option.
33 See
<a class=
"reference internal" href=
"#eq-m">eq:M
</a> and
<a class=
"reference internal" href=
"#eq-schrodinger">eq:schrödinger
</a> below.
</p>
34 <p>The determinant of the matrix
</p>
35 <div class=
"math" id=
"eq-m">
37 \mathbf{M} = \left(\begin{matrix}a
&b\\c
&d\end{matrix}\right)
40 <p>is
<span class=
"math">\(|\mathbf{M}| = ad - bc\)
</span>
42 <p>More than one display math block can be put in one math directive.
43 For example, the following sum and integral with limits:
</p>
46 \int_0^
1 x^n dx = \frac{
1}{n +
1}
51 \sum_{n=
1}^m n = \frac{m(m+
1)}{
2}
54 <p>LaTeX-supported Unicode math symbols can be used in math roles and
56 <p>The Schrödinger equation
</p>
57 <div class=
"math" id=
"eq-schrodinger">
59 i\hbar \frac{\partial }{\partial t}\Psi = \hat{H}\Psi ,
62 <p>with the
<em>wave function
</em> <span class=
"math">\(\Psi \)
</span>
63 , describes how the quantum state of a
64 physical system changes in time.
</p>
66 <dt>Math-Accents:
</dt>
67 <dd><table border=
"1" class=
"borderless first last docutils">
74 <tr><td><span class=
"math">\(\acute{a}\)
</span>
75 <tt class=
"docutils literal">\acute{a}
</tt></td>
76 <td><span class=
"math">\(\dot{t}\)
</span>
77 <tt class=
"docutils literal">\dot{t}
</tt></td>
78 <td><span class=
"math">\(\hat{\gamma}\)
</span>
79 <tt class=
"docutils literal"><span class=
"pre">\hat{\gamma}
</span></tt></td>
81 <tr><td><span class=
"math">\(\grave{a}\)
</span>
82 <tt class=
"docutils literal">\grave{a}
</tt></td>
83 <td><span class=
"math">\(\ddot{t}\)
</span>
84 <tt class=
"docutils literal">\ddot{t}
</tt></td>
85 <td><span class=
"math">\(\tilde{\alpha}\)
</span>
86 <tt class=
"docutils literal"><span class=
"pre">\tilde{\alpha}
</span></tt></td>
88 <tr><td><span class=
"math">\(\breve{x}\)
</span>
89 <tt class=
"docutils literal">\breve{x}
</tt></td>
90 <td><span class=
"math">\(\dddot{t}\)
</span>
91 <tt class=
"docutils literal">\dddot{t}
</tt></td>
92 <td><span class=
"math">\(\vec{\imath}\)
</span>
93 <tt class=
"docutils literal"><span class=
"pre">\vec{\imath}
</span></tt></td>
95 <tr><td><span class=
"math">\(\check{a}\)
</span>
96 <tt class=
"docutils literal">\check{a}
</tt></td>
97 <td><span class=
"math">\(\bar{a}\)
</span>
98 <tt class=
"docutils literal">\bar{a}
</tt></td>
99 <td><span class=
"math">\(\vec{R}\)
</span>
100 <tt class=
"docutils literal">\vec{R}
</tt></td>
108 <p>Modulation Transfer Function:
</p>
111 \text{MTF} = \left|\frac{\mathcal{F}\{s(x)\}}
112 {\mathcal{F}\{ s(x)\} |_{\omega _{x}=
0}}\right|
113 = \mathrm{abs}\left(\frac
114 {\int _{-\infty }^{\infty }s(x) \mathrm{e}^{\mathrm{i}\omega _{x}x}\mathrm{d}{x}}
115 {\int _{-\infty }^{\infty }s(x)\mathrm{d}{x}}
119 <p>Math split over two lines: If a double backslash is detected outside a
120 <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>
121 <tt class=
"docutils literal">align
</tt> environment:
</p>
124 s_{\mathrm{out}}(x)
& = s_{\mathrm{in}}(x') * s_\delta (x-x') \\
125 & = \int s_{\mathrm{in}}(x')s_\delta (x-x')\mathrm{d}x'
128 <p>Cases (
"manually
", with
<tt class=
"docutils literal">matrix
</tt> environment):
</p>
131 \mathrm{sgn}(x) = \left\{\begin{matrix}
137 <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
138 HTML writers with
<tt class=
"docutils literal"><span class=
"pre">--math-output=MathML
</span></tt>):
</p>
141 \mathrm{sgn}(x) = \begin{cases}