MATH 251 Lecture Notes - Fourier Series, Periodic Function, Trigonometric Series
Document Summary
Even and odd functions; cosine and sine series extensions; particular solution of the heat conduction equation. Suppose f is a periodic function with a period t = 2l. Then the fourier series representation of f is a trigonometric series (that is, it is an infinite series consists of sine and cosine terms) of the form xf a. Where the coefficients are given by the euler-fourier formulas: a m b n. , m = 0, 1, 2, 3, sin)( xf xn. The coefficients a"s are called the fourier cosine coefficients (including a0, the constant term, which is in reality the 0-th cosine term), and b"s are called the fourier sine coefficients. Note 1: thus, every periodic function can be decomposed into a sum of one or more cosine and/or sine terms of selected frequencies determined solely by that of the original function.
