# Mathematics

Docutils supports inline math with the prefix or postfix `:math:` role specificator, n! + sin(x2n) and Ac=(π)/(4)d2, as well as displayed math via the math directive:

f(ϵ) =(1)/(1 + exp⎛⎝(ε)/(kBT)⎞⎠)

Content may start on the first line of the directive, e.g.

N=(number of apples)/(7)

Equations can be labeled with a reference name using the `:name:` option. See eq:M and eq:schrödinger below.

The determinant of the matrix

M=⎛⎜⎝ a b c d ⎞⎟⎠

is |M| =ad−bc.

More than one display math block can be put in one math directive. For example, the following sum and integral with limits:

1∫0xndx=(1)/(n+ 1)
m∑n= 1n=(m(m+ 1))/(2)

LaTeX-supported Unicode math symbols can be used in math roles and directives:

The Schrödinger equation

iħ(∂)/(∂t)Ψ =ĤΨ,

with the wave function Ψ, describes how the quantum state of a physical system changes in time.

Math-Accents:

  á `\acute{a}` | ṫ `\dot{t}` | γ̂ `\hat{\gamma}`
  à `\grave{a}` | ẗ `\ddot{t}` | α̃ `\tilde{\alpha}`
  x̆ `\breve{x}` | ⋯t `\dddot{t}` | →ı `\vec{\imath}`
  ǎ `\check{a}` | ‒a `\bar{a}` | →R `\vec{R}`

Modulation Transfer Function:

MTF=||(ℱ{s(x)})/(ℱ{s(x)}|ωx= 0)||=abs⎛⎝(∫∞− ∞s(x)eiωxxdx)/(∫∞− ∞s(x)dx)⎞⎠.

Math split over two lines: If a double backslash is detected outside a `\begin{...} \end{...}` pair, the math code is wrapped in an AMSmath `align` environment:

sout(x) =sin(x’)*sδ(x−x’) =∫sin(x’)sδ(x−x’)dx’

Cases with the AMSmath `cases` environment:

sgn(x) =⎧⎨⎩ − 1 x< 0 −1 x> 0