Trigonometric Fourier Series

Abstract

A function f(x) is called periodic if there exists a constant T > o for which f(x+T)=f(x) for any x. The constant T is called the period of the function f(x). The most familiar periodic functions are sin x, cos x, tan x, etc. Periodic functions arise in many applications of mathematics to problems of physics and engineering. Expressing these periodic functions in terms of a Fourier series is a great tool in solving m a n y of these problems. If we plot a periodic function y = f(x) o n any closed interval a x a + T, we can obtain the entire graph of f(x) b y periodic repetition of the portion of the curve represented in the interval a f x < a + T. (see Fig. I)