Engineering Mathematics, Volume 2

8

Fourier Series

8.1 Introduction

Fourier series¹ is an important tool in solving problems in conduction of heat, electrical engineering, current and voltage in alternating circuits, electrodynamics, acoustics, etc. The basic idea is to represent periodic functions by a series involving sines and cosines. In this chapter, we find expansions of even/odd functions first in an interval of 2π and later of 2l Finally, we develop half-range Fourier series also.

First we begin with the notion of periodic functions; and even and odd functions.

8.2 Periodic Functions, Properties

The graph of a trigonometric function repeats itself in regular intervals. Such functions are called periodic functions.

Periodic Function: Definition A function f(x) is called ...