082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

6 Sequencesandseries
Contents 6.1 Introduction 200
6.2 Sequences 201
6.3 Series 209
6.4 Thebinomialtheorem 214
6.5 Powerseries 218
6.6 Sequencesarisingfromtheiterativesolutionofnon-linearequations 219
Reviewexercises6 222
6.1 INTRODUCTION
Muchofthematerialinthischapterisofafundamentalnatureandisapplicabletomany
differentareasofengineering.Forexample,ifcontinuoussignalsorwaveforms,suchas
those described in Chapter 2, are sampled at periodic intervals we obtain a sequence of
measuredvalues.Sequencesalsoarisewhenweattempttoobtainapproximatesolutions
of equations which model physical phenomena. Such approximations are necessary if
a solution is to be obtained using a digital computer. For many problems of practical
interest to engineers a computer solution is the only possibility. The z transform is an
exampleofaninfiniteserieswhichisparticularlyimportantinthefieldofdigitalsignal
processing. Signal processing is concerned with modifying signals in order to improve
them in some way. For example, the signals received from space satellites have to undergo
extensive processing in order to counteract the effects of noise, and to filter out
unwanted frequencies, before they can provide, say, acceptable visual images. Digital
signal processing is signal processing carried out using a computer. So, skill in manipulating
sequences and series is crucial. Later chapters will develop these concepts and
show examples of their use insolving real engineering problems.