Introduction

In this Section we show how a periodic function can be expressed as a series of sines and cosines. We begin by obtaining some standard integrals involving sinusoids. We then assume that if f ( t ) is a periodic function, of period 2 π , then the Fourier series expansion takes the form:

f ( t ) = a 0 2 + n = 1 ( a n cos n t + b n sin n t )

Our main purpose here is to show how the constants in this expansion, a n (for n = 0 , 1 , 2 , 3 and b n (for n = 1 , 2 , 3 , ), may be determined for any given function f ( t ) .

Prerequisites

Learning Outcomes

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