Advanced Engineering Mathematics, 7th Edition

12.3 Fourier Cosine and Sine Series

INTRODUCTION

The effort expended in the evaluation of coefficients a₀, a_n , and b_n in expanding a function f in a Fourier series is reduced significantly when f is either an even or an odd function. A function f is said to be

even if f(–x) = f(x) and odd if f(–x) = –f(x).

On a symmetric interval such as (–p, p), the graph of an even function possesses symmetry with respect to the y-axis, whereas the graph of an odd function possesses symmetry with respect to the origin.

Even and Odd Functions

It is likely the origin of the words even and odd derives from the fact that the graphs of polynomial functions ...