- #1

mathman

Science Advisor

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Laplace transform (function f(x) defined from 0 to inf) integral of f(x)e

^{-xt}, defined for t>=0.

Fourier transform (function f(x) defined from -inf to inf) integral of f(x)e

^{-itx}defined for all real t.

Complex Fourier series (function f(x) defined on finite interval - simplify by making it (0,1)) Coeficients (c

_{n}) are given by integral of f(x)e

^{-2(pi)inx}, where n ranges over all integers. The series terms are c

_{n}e

^{2(pi)nx}

Real Fourier series use sin and cos instead of exp function.