Programming Mathematics Using MATLAB

273 Pages·2020·7.443 MB·English

by  Lisa A. Oberbroeckling

PROGRAMMING
MATHEMATICS
®
USING MATLAB

PROGRAMMING
MATHEMATICS USING
®
MATLAB
LISAA.OBERBROECKLING
DepartmentofMathematicsandStatistics
LoyolaUniversityMaryland
Baltimore,MD,UnitedStates
AcademicPressisanimprintofElsevier
125LondonWall,LondonEC2Y5AS,UnitedKingdom
525BStreet,Suite1650,SanDiego,CA92101,UnitedStates
50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates
TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom
Copyright©2021ElsevierInc.Allrightsreserved.
MATLAB®isatrademarkofTheMathWorks,Inc.andisusedwithpermission.
TheMathWorksdoesnotwarranttheaccuracyofthetextorexercisesinthisbook.
Thisbook’suseordiscussionofMATLAB®softwareorrelatedproductsdoesnotconstituteendorsementor
sponsorshipbyTheMathWorksofaparticularpedagogicalapproachorparticularuseoftheMATLAB®software.
Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor
mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,without
permissioninwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthe
Publisher’spermissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearanceCenter
andtheCopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions.
ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(other
thanasmaybenotedherein).
Notices
Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour
understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusingany
information,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodsthey
shouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhaveaprofessional
responsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability
foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,or
fromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein.
LibraryofCongressCataloging-in-PublicationData
AcatalogrecordforthisbookisavailablefromtheLibraryofCongress
BritishLibraryCataloguing-in-PublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN:978-0-12-817799-0
ForinformationonallAcademicPresspublications
visitourwebsiteathttps://www.elsevier.com/books-and-journals
Publisher:KateyBirtcher
EditorialProjectManager:RafaelG.Trombaco
ProductionProjectManager:BeulaChristopher
Designer:BridgetHoette
TypesetbyVTeX
To Rob and James, for the support, patience (especially when teaching MATLAB), and
laughter.
To Christos Xenophontos for your encouragement and for introducing me to MATLAB.
Contents
Preface xiii
Introduction xv
Part1. MATLAB®
1. IntroductiontoMATLAB® 3
1.1. BasicMATLAB®information 3
1.1.1. StartingMATLAB 3
1.1.2. Goodcommandstoknow 3
1.2. Basicmathematics 4
1.2.1. Built-inmathematicalfunctions 5
1.2.2. Precedencerules 6
1.2.3. Formats 8
1.3. Variables 9
1.4. Diariesandscriptfiles 10
1.5. Exercises 12
2. VectorsandMatrices(Arrays) 15
2.1. One-dimensionalarrays(vectors) 15
2.1.1. Constantspacedvectors 15
2.1.2. Equallyspacedvectors 16
2.2. Two-dimensionalarrays(matrices) 17
2.3. Addressingelementsofvectors/arrays 18
2.4. Component-wisecalculations 22
2.5. Randomnumbers 25
2.6. Exercises 28
3. PlottinginMATLAB® 33
3.1. Basic2Dplots 33
3.2. Baddomainexamples 34
3.3. Axissettings 35
3.4. Multipleplots 40
3.5. Color,line,andmarkermodifications 43
3.5.1. Clf/closeall 46
3.5.2. Subplots 46
3.6. Other2Dplots 49
3.6.1. Parametriccurves 49
3.6.2. Polarcurves 50
3.7. Exercises 52
4. Three-DimensionalPlots 59
4.1. Vectorfunctionsorspacecurves 59
vii
viii Contents
4.2. Plottingsurfaces 62
4.2.1. Themeshgridcommand 63
4.2.2. Domainissues 64
4.2.3. Levelcurves 65
4.2.4. Multipleplotsandmodifyingcolors 66
4.3. Viewcommand 68
4.4. Axissettings,revisited 70
4.5. Othercoordinatesystemsand3Dgraphs 72
4.5.1. Thesphereandcylindercommands 72
4.5.2. Cylindricalcoordinates 75
4.5.3. Sphericalcoordinates 77
4.6. Exercises 78
5. Functions 83
5.1. Thelookforandhelpcommands 83
5.2. Fileformat 84
5.3. Functionexamples 86
5.3.1. Basicfunctionexamples 86
5.3.2. Morefunctionexamples–multipleinputs 86
5.3.3. Multipleoutputs 87
5.3.4. Badexamples 89
5.4. Exercises 90
6. ControlFlow 93
6.1. Relationalandlogicaloperators 93
6.2. Ifstatements 97
6.3. Switch/case 99
6.4. Useofcharacteristicfunctions 99
6.5. Forloops 100
6.6. Whileloops 102
6.7. Usefulcommandsbreak,continue,return,anderror 103
6.8. Optionalinputsandoutputsoffunctions 104
6.9. Exercises 107
7. MiscellaneousCommandsandCodeImprovement 115
7.1. Miscellaneouscommands 115
7.1.1. Thefprintfcommand 115
7.1.2. Thesprintfcommand 117
7.1.3. Formatsrevisited 118
7.1.4. Thesave/loadcommands 118
7.1.5. Thetic/toccommands 119
7.1.6. Thefillcommand 119
7.1.7. Thecommandalpha 122
7.1.8. Thesyms,diff,int,andsubscommands 125
7.1.9. Commandsforpolynomials 127
Contents ix
7.2. Codeimprovement 129
7.2.1. Vectorizationofcode 130
7.2.2. Preallocation 131
Part2. MathematicsandMATLAB®
8. TransformationsandFernFractals 135
8.1. Lineartransformations 135
8.2. Affinetransformations 139
8.3. Fernfractals 140
8.4. Exercises 141
9. ComplexNumbersandFractals 147
9.1. Complexnumbers 147
9.1.1. Addingcomplexnumbers 147
9.1.2. Multiplicationbyarealnumbers(scalars) 147
9.1.3. MultiplicationanddeMoivre’stheorem/formula 147
9.1.4. PlottingcomplexnumbersinMATLAB® 150
9.1.5. Creatinglinesegmentswithcomplexnumbers 151
9.2. TheChaosGame 153
9.3. Linereplacementfractals 154
9.3.1. Snowflakefractals 154
9.3.2. GosperIsland 155
9.4. Geometricseries 156
9.5. Exercises 158
10.SeriesandTaylorPolynomials 167
10.1. Reviewofseries 167
10.2. Powerseries 169
10.3. TaylorpolynomialsandTaylorseries 173
10.4. Exercises 177
11.NumericalIntegration 183
11.1. Approximatingintegrals/numericalintegration 183
11.2. Riemannsums 183
11.3. Errorbounds 185
11.4. Simpson’srule 186
11.5. Exercises 189
12.TheGram–SchmidtProcess 193
12.1. Generalvectorspacesandsubspaces 193
12.1.1. Vectorspaces 193
12.1.2. Subspaces 194
12.2. Linearcombinationsofvectors 195
12.3. Linearindependenceandbases 196
x Contents
12.3.1. Linearindependence 196
12.3.2. Bases 197
12.4. Rank 200
12.5. OrthonormalvectorsandtheGram–Schmidtprocess 201
12.5.1. Orthogonalandorthonormalvectors 201
12.5.2. TheGram–Schmidtprocess 204
12.6. Answerstoexampleproblems 210
12.7. Exercises 211
A. PublishingandLiveScripts 215
A.1. Livescripts 215
A.2. BasicscriptsorM-files 215
A.3. PublishingM-files 216
A.4. Usingsections 216
A.4.1. Usingsectionsforpublishing 217
A.4.2. Usingsectionsforrunning/debuggingfiles 222
A.5. Formattingtext 223
A.5.1. Basictextformatting 223
A.5.2. Lists 224
A.5.3. HTMLlinks 225
A.5.4. Insertingimages 225
A.5.5. Pre-formattedtext 226
A.5.6. InsertingHTMLcode 227
A.5.7. InsertingLATEXequations 227
B. FinalProjects 229
B.1. Ciphers 229
B.1.1. Substitutioncipher 229
B.1.2. Columnartranspositioncipher 230
B.2. GameofPig 231
B.3. LinearizationandNewton’smethod 232
B.3.1. Linearization 232
B.3.2. Newton’smethod 232
B.4. DiskandShellmethod 234
B.5. Powerballdata 235
C. LinearAlgebraProjects 237
C.1. Matrixcalculationsandlinearsystems 237
C.1.1. Firsthandout 237
C.1.2. Exercises 239
C.2. TheHillcipher 243
C.2.1. Usefulcommands 245
C.2.2. Exercises 251
C.3. Least-squaressolutions 252
C.3.1. Briefoverview 252