Applied Math

Fourier series represents periodic functions as infinite sums of sines and cosines. Any periodic function can be decomposed into oscillatory components.

A differential equation relates an unknown function to its derivatives. It's a fundamental tool for modeling physical phenomena.

Complex analysis studies calculus of complex-valued functions. Analytic functions are differentiable and have beautiful properties.

Game theory mathematically analyzes strategic interactions. It predicts outcomes when players act rationally.

Cryptography uses mathematical techniques for secure communication. It's based on number theory, algebra, and complexity theory.

Transforms time-domain functions to frequency domain, converting differential equations to algebraic equations.

An optimization algorithm that iteratively moves in the opposite direction of the gradient to find the minimum.

A numerical method to iteratively approximate roots of equations using tangent lines.

A mathematical method to optimize a linear objective function subject to linear constraints.