### Introduction

In this Section we address the following problem:

Can we find a Fourier series expansion of a function defined over a finite interval?

Of course we recognise that such a function could not be periodic (as periodicity demands an infinite interval). The answer to this question is yes but we must first convert the given non-periodic function into a periodic function. There are many ways of doing this. We shall concentrate on the most useful extension to produce a so-called half-range Fourier series .

#### Prerequisites

• know how to obtain a Fourier series
• be familiar with odd and even functions and their properties
• have knowledge of integration by parts

#### Learning Outcomes

• choose to expand a non-periodic function either as a series of sines or as a series of cosines