calculus
Finite Difference Approximations
$$\frac{f(x+h) - 2f(x) + f(x-h)}{h^2}$$
Taylor & Maclaurin Series
$$f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} \cdot (x - a)^n$$
Feynmann's Trick For Exponential Integrals
$$\int_0^{\infty} x^n e^{-tx} dx = \frac{n!}{t^{n+1}}$$
Convolution
$$(f*g)(t)=\int_{-\infty}^{\infty} f(\tau)g(t-\tau)d\tau$$
L'Hopital's Rule
$$\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$$
Green's Theorem
$$\small \oint_C Pdx + Qdy = \iint_D \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} dA$$
Stokes' Theorem
$$\int_C \vec{F} \cdot d\vec{r} = \iint_S \nabla \times \vec{F} \cdot d\vec{S}$$
Definition of the Derivative
$$\frac{d}{dx}f(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$
Fundamental Theorem of Calculus
$$\int_a^b f(x) dx = F(b) - F(a)$$
Maclaurin Series for exp(x)
$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$