Engineering Mathematics

1024 Pages·2017·9.567 MB·English

by  Anthony Croft, Robert Davison, Martin Hargreaves, James Flint

ENGINEERING
MATHEMATICS
A Foundation for Electronic, Electrical,
Communications and Systems Engineers
FIFTH EDITION
Anthony Croft (cid:127) Robert Davison
Martin Hargreaves (cid:127) James Flint
Engineering Mathematics
At Pearson, we have a simple mission: to help people
make more of their lives through learning.
We combine innovative learning technology with trusted
content and educational expertise to provide engaging
and effective learning experiences that serve people
wherever and whenever they are learning.
From classroom to boardroom, our curriculum materials, digital
learning tools and testing programmes help to educate millions
of people worldwide – more than any other private enterprise.
Every day our work helps learning flourish, and
wherever learning flourishes, so do people.
To learn more, please visit us at www.pearson.com/uk
Fifth Edition
Engineering Mathematics
A Foundation for Electronic, Electrical,
Communications and Systems Engineers
Anthony Croft
LoughboroughUniversity
Robert Davison
Martin Hargreaves
CharteredPhysicist
James Flint
LoughboroughUniversity
Harlow, England • London • New York • Boston • San Francisco • Toronto • Sydney
Dubai • Singapore • Hong Kong • Tokyo • Seoul • Taipei • New Delhi
Cape Town • São Paulo • Mexico City • Madrid • Amsterdam • Munich • Paris • Milan
PEARSONEDUCATIONLIMITED
EdinburghGate
HarlowCM202JE
UnitedKingdom
Tel:[phone]
Web:www.pearson.com/uk
FirsteditionpublishedundertheAddison-Wesleyimprint1992(print)
SecondeditionpublishedundertheAddison-Wesleyimprint1996(print)
ThirdeditionpublishedunderthePrenticeHallimprint2001(print)
Fourtheditionpublished2013(printandelectronic)
Fiftheditionpublished2017(printandelectronic)
©Addison-WesleyPublishersLimited1992,1996(print)
©PearsonEducationLimited2001(print)
©PearsonEducationLimited2013,2017(printandelectronic)
TherightsofAnthonyCroft,RobertDavison,MartinHargreavesandJamesFlint
tobeidentifiedasauthorsofthisworkhavebeenassertedbythemin
accordancewiththeCopyright,DesignsandPatentsAct1988.
Theprintpublicationisprotectedbycopyright.Priortoanyprohibitedreproduction,
storageinaretrievalsystem,distributionortransmissioninanyformorbyanymeans,
electronic,mechanical,recordingorotherwise,permissionshouldbeobtainedfrom
thepublisheror,whereapplicable,alicencepermittingrestrictedcopyinginthe
UnitedKingdomshouldbeobtainedfromtheCopyrightLicensingAgencyLtd,
Barnard’sInn,86FetterLane,LondonEC4A1EN.
TheePublicationisprotectedbycopyrightandmustnotbecopied,reproduced,transferred,
distributed,leased,licensedorpubliclyperformedorusedinanywayexceptasspecifically
permittedinwritingbythepublishers,asallowedunderthetermsandconditionsunderwhich
itwaspurchased,orasstrictlypermittedbyapplicablecopyrightlaw.Anyunauthorised
distributionoruseofthistextmaybeadirectinfringementoftheauthors’andthepublisher’s
rightsandthoseresponsiblemaybeliableinlawaccordingly.
PearsonEducationisnotresponsibleforthecontentofthird-partyinternetsites.
ISBN:978-1-292-14665-2(print)
978-1-292-14667-6(PDF)
978-1-292-14666-9(ePub)
BritishLibraryCataloguing-in-PublicationData
AcataloguerecordfortheprinteditionisavailablefromtheBritishLibrary
LibraryofCongressCataloging-in-PublicationData
Names:Croft,Tony,1957–author.
Title:Engineeringmathematics:afoundationforelectronic,electrical,
communicationsandsystemsengineers/AnthonyCroft,Loughborough
University,RobertDavison,DeMontfortUniversity,MartinHargreaves,
DeMontfortUniversity,JamesFlint,LoughboroughUniversity.
Description:Fifthedition.|Harlow,England;NewYork:Pearson,2017.k
Revisededitionof:Engineeringmathematics:afoundationforelectronic,
electrical,communications,andsystemsengineers/AnthonyCroft,Robert
Davison,MartinHargreaves.3rdediton.2001.|Includesindex.
Identifiers:LCCN2017011081|ISBN9781292146652(Print)|ISBN9781292146676
(PDF)|ISBN9781292146669(ePub)
Subjects:LCSH:Engineeringmathematics.|Electrical
engineering–Mathematics.|Electronics–Mathematics.
Classification:LCCTA330.C762017|DDC510–dc23
LCrecordavailableathttps://lccn.loc.gov/2017011081
AcatalogrecordfortheprinteditionisavailablefromtheLibraryofCongress
10 9 8 7 6 5 4 3 2 1
21 20 19 18 17
Printeditiontypesetin10/12TimesRomanbyiEnerzigerAptara®,Ltd.
PrintedinSlovakiabyNeografia
NOTETHATANYPAGECROSSREFERENCESREFERTOTHEPRINTEDITION
To Kate, Tom and Harvey -- A.C.
To Kathy -- R.D.
To my father and mother -- M.H.
To Suzanne, Alexandra and Dominic -- J.F.
Contents
Preface xvii
Acknowledgements xix
Chapter 1 Review of algebraic techniques
1
1.1 Introduction 1
1.2 Lawsofindices 2
1.3 Numberbases 11
1.4 Polynomialequations 20
1.5 Algebraicfractions 26
1.6 Solutionofinequalities 33
1.7 Partialfractions 39
1.8 Summationnotation 46
Reviewexercises1 50
Chapter 2 Engineering functions
54
2.1 Introduction 54
2.2 Numbersandintervals 55
2.3 Basicconceptsoffunctions 56
2.4 Reviewofsomecommonengineeringfunctionsandtechniques 70
Reviewexercises2 113
Chapter 3 The trigonometric functions
115
3.1 Introduction 115
3.2 Degreesandradians 116
3.3 Thetrigonometricratios 116
3.4 Thesine,cosineandtangentfunctions 120
3.5 Thesincxfunction 123
3.6 Trigonometricidentities 125
3.7 Modellingwavesusingsint andcost 131
3.8 Trigonometricequations 144
Reviewexercises3 150
viii Contents
Chapter 4 Coordinate systems
154
4.1 Introduction 154
4.2 Cartesiancoordinatesystem–twodimensions 154
4.3 Cartesiancoordinatesystem–threedimensions 157
4.4 Polarcoordinates 159
4.5 Somesimplepolarcurves 163
4.6 Cylindricalpolarcoordinates 166
4.7 Sphericalpolarcoordinates 170
Reviewexercises4 173
Chapter 5 Discrete mathematics
175
5.1 Introduction 175
5.2 Settheory 175
5.3 Logic 183
5.4 Booleanalgebra 185
Reviewexercises5 197
Chapter 6 Sequences and series
200
6.1 Introduction 200
6.2 Sequences 201
6.3 Series 209
6.4 Thebinomialtheorem 214
6.5 Powerseries 218
6.6 Sequencesarisingfromtheiterativesolution
ofnon-linearequations 219
Reviewexercises6 222
Chapter 7 Vectors
224
7.1 Introduction 224
7.2 Vectorsandscalars:basicconcepts 224
7.3 Cartesiancomponents 232
7.4 Scalarfieldsandvectorfields 240
7.5 Thescalarproduct 241
7.6 Thevectorproduct 246
7.7 Vectorsofndimensions 253
Reviewexercises7 255
Chapter 8 Matrix algebra
257
8.1 Introduction 257
8.2 Basicdefinitions 258
Contents ix
8.3 Addition,subtractionandmultiplication 259
8.4 Usingmatricesinthetranslationandrotationofvectors 267
8.5 Somespecialmatrices 271
8.6 Theinverseofa2 2matrix 274
×
8.7 Determinants 278
8.8 Theinverseofa3 3matrix 281
×
8.9 Applicationtothesolutionofsimultaneousequations 283
8.10 Gaussianelimination 286
8.11 Eigenvaluesandeigenvectors 294
8.12 Analysisofelectricalnetworks 307
8.13 Iterativetechniquesforthesolutionofsimultaneousequations 312
8.14 Computersolutionsofmatrixproblems 319
Reviewexercises8 321
Chapter 9 Complex numbers
324
9.1 Introduction 324
9.2 Complexnumbers 325
9.3 Operationswithcomplexnumbers 328
9.4 Graphicalrepresentationofcomplexnumbers 332
9.5 Polarformofacomplexnumber 333
9.6 Vectorsandcomplexnumbers 336
9.7 Theexponentialformofacomplexnumber 337
9.8 Phasors 340
9.9 DeMoivre’stheorem 344
9.10 Lociandregionsofthecomplexplane 351
Reviewexercises9 354
Chapter 10 Differentiation
356
10.1 Introduction 356
10.2 Graphicalapproachtodifferentiation 357
10.3 Limitsandcontinuity 358
10.4 Rateofchangeataspecificpoint 362
10.5 Rateofchangeatageneralpoint 364
10.6 Existenceofderivatives 370
10.7 Commonderivatives 372
10.8 Differentiationasalinearoperator 375
Reviewexercises10 385
Chapter 11 Techniques of differentiation
386
11.1 Introduction 386
x Contents
11.2 Rulesofdifferentiation 386
11.3 Parametric,implicitandlogarithmicdifferentiation 393
11.4 Higherderivatives 400
Reviewexercises11 404
Chapter 12 Applications of differentiation
406
12.1 Introduction 406
12.2 Maximumpointsandminimumpoints 406
12.3 Pointsofinflexion 415
12.4 TheNewton–Raphsonmethodforsolvingequations 418
12.5 Differentiationofvectors 423
Reviewexercises12 427
Chapter 13 Integration
428
13.1 Introduction 428
13.2 Elementaryintegration 429
13.3 Definiteandindefiniteintegrals 442
Reviewexercises13 453
Chapter 14 Techniques of integration
457
14.1 Introduction 457
14.2 Integrationbyparts 457
14.3 Integrationbysubstitution 463
14.4 Integrationusingpartialfractions 466
Reviewexercises14 468
Chapter 15 Applications of integration
471
15.1 Introduction 471
15.2 Averagevalueofafunction 471
15.3 Rootmeansquarevalueofafunction 475
Reviewexercises15 479
Chapter 16 Further topics in integration
480
16.1 Introduction 480
16.2 Orthogonalfunctions 480
16.3 Improperintegrals 483
16.4 Integralpropertiesofthedeltafunction 489
16.5 Integrationofpiecewisecontinuousfunctions 491
16.6 Integrationofvectors 493
Reviewexercises16 494