Here are a few LaTeX snippets that folks in PDEs might find useful.
PDEs
First order
u_t + 2 u_x = 0
$u_t + 2 u_x = 0$
Second order
u_t = \alpha u_{xx}
$u_t = \alpha u_{xx}$
Display mode
u_{tt} = c^2 \Delta u = c^2 (u_{xx} + u_{yy})
$$
u_{tt} = c^2 \Delta u = c^2 (u_{xx} + u_{yy})
$$
Not so complicated functions
Polynomials
f(x) = x^2 + 2x + 1
$f(x) = x^2 + 2x + 1$
Trig functions
g(x) = \sin(\pi x)
$g(x) = \sin(\pi x)$
More complicated functions
Exponentials
e^{-x^2}
$e^{-x^2}$
Fractions
\frac{x}{(1+x^2)^3}
$$
\frac{x}{(1+x^2)^3}
$$
The normal distribution / heat kernel
\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}
$$
\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}
$$