MathJax Examples

Adapted from https://www.mathjax.org/#samples.

Fonts

\(\mathbb{R}\), \(\mathcal{R}\)

The Quadratic Formula

\[x = {-b \pm \sqrt{b^2-4ac} \over 2a}\]

Cauchy's Integral Formula

\[f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz\]

Angle Sum Formula for Cosines

\[ \cos(\theta+\phi)=\cos(\theta)\cos(\phi)−\sin(\theta)\sin(\phi) \]

Gauss' Divergence Theorem

\[ \int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS \]

Curl of a Vector Field

\[ \vec{\nabla} \times \vec{F} = \left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i} + \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j} + \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k} \]

Standard Deviation

\[\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2} \]

Definition of Christoffel Symbols

\[(\nabla_X Y)^k = X^i (\nabla_i Y)^k = X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)\]