Half-RangeSeries.PDFVIP

Half-Range Series 23.5 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. • know how to obtain a Fourier series Prerequisites • be familiar with odd and even functions and their properties Before starting this Section you should . . . • have knowledge of integration by parts • choose to expand a non-periodic function Learning Outcomes either as a series of sines or as a series of cosines On completion you should be able to . . . 46 HELM (2008): Workbook 23: Fourier Series ® 1. Half-range Fourier series So far we have shown how to represent given periodic functions by Fourier series. We no