mathematics
Vector Calculus Product Rules
$$\nabla (fg) = f(\nabla g) + g(\nabla f)$$
Error Function
$$\text{erf}(z) = \frac{2}{\sqrt{\pi}} \int_0^z e^{-t^2} dt$$
Log Laws
$$\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$$
De Moivre's Theorem
$$\small (\cos x+ i \sin x)^n=\cos(nx)+i\sin(nx)$$
Taylor & Maclaurin Series
$$f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} \cdot (x - a)^n$$
Bayes' Theorem
$$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$