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Equation examples

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


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

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