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