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

2 Engineeringfunctions
Contents 2.1 Introduction 54
2.2 Numbersandintervals 55
2.3 Basicconceptsoffunctions 56
2.4 Reviewofsomecommonengineeringfunctionsandtechniques 70
Reviewexercises2 113
2.1 INTRODUCTION
The study of functions is central to engineering mathematics. Functions can be used to
describe the way quantities change: for example, the variation in the voltage across an
electroniccomponentwithtime,thevariationinpositionofanelectricmotorwithtime
and the variation inthe strengthof a signalwith both position and time.
Inthischapterweintroduceseveralconceptsassociatedwithfunctionsbeforegoing
ontocatalogue anumber ofengineering functions inSection2.4.Muchofthematerial
ofSection2.4willalreadybefamiliartothereaderandsothissectionshouldbetreated
asareferencesectiontobedippedintowhenevernecessary.Anumberofmathematical
methods are also included in Section 2.4, most of which will be familiar but they have
been collected together inorder tomake the book complete.
When trying to understand a mathematical function it is always useful to sketch a
graphinordertoobtainanideaofitsbehaviour.Thereaderisencouragedtosketchsuch
graphs whenever a new function is met. Graphics calculators are now readily available
andtheymakethistaskrelativelyeasy.Ifyoupossesssuchacalculatorthenitwouldbe
useful to make use of it whenever a new function is introduced. Software packages are
alsoavailabletoallowsuchplotstobecarriedoutonacomputer.Thesecanbeusefulfor
plotting more complicated functions and ones that depend on more than one variable.
We examine functions of more than one variable inChapter 25.
Throughoutthebookwemakeuseofthetermmathematicalmodel.Whendoingso
wemeananidealizationofanengineeringsystemoraphysicalsituationsothatitcanbe
describedbymathematicalequations.Toreflectanengineeringsystemveryaccurately,
a sophisticated model, consisting of many interrelated equations, may be needed. Although
accurate, such a model may be cumbersome to use. Accuracy can be sacrificed