Math, chemistry and physics

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Math

Inline: the mass–energy relation $E = mc^2$. As a block, the Gaussian integral:

$\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}$

And a sum:

$\sum_{k=1}^{n} k = \frac{n(n+1)}{2}$

Physics

The time-dependent Schrödinger equation in standard notation:

$i\hbar\,\frac{\partial}{\partial t}\lvert\psi\rangle = \hat{H}\lvert\psi\rangle$

Maxwell, differential form:

$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$

Chemistry

Via the mhchem extension with \ce{}:

$\ce{CH4 + 2 O2 -> CO2 + 2 H2O}$

$\ce{2 H2 + O2 <=> 2 H2O}$