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Mathematical Methods by E. Rukmangadachari

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10

Fourier Series

10.1 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 expansion 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.

10.2 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 (

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