MATLAB Programming: Mathematical Problem Solutions (De Gruyter STEM)

322 Pages·2020·10.188 MB·English

by  Dingyü Xue

DingyüXue
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Dingyü Xue
®
MATLAB
Programming
|
Mathematical Problem Solutions
Author
Prof.DingyüXue
SchoolofInformationScienceandEngineering
NortheasternUniversity
WenhuaRoad3rdStreet
110819Shenyang
China
[email protected]
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softwareorrelatedproductsdoesnotconstituteendorsementorsponsorshipbyTheMathWorksof
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LibraryofCongressControlNumber:2019955271
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
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detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2020TsinghuaUniversityPressLimitedandWalterdeGruyterGmbH,Berlin/Boston
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Preface
Scientificcomputingiscommonlyandinevitablyencounteredincourselearning,sci-
entificresearchandengineeringpracticeforeachscientificandengineeringstudent
andresearcher.Forthestudentsandresearchersinthedisciplineswhicharenotpure
mathematics,itisusuallynotawisethingtolearnthoroughlylow-leveldetailsofre-
latedmathematicalproblems,andalsoitisnotasimplethingtofindsolutionsofcom-
plicatedproblemsbyhand.Itisaneffectivewaytotacklescientificproblems,with
highefficiencyandin accurateand creativemanner,withthe mostadvancedcom-
putertools.Thismethodisespeciallyusefulinsatisfyingtheneedsforthoseinthe
areaofscienceandengineering.
Theauthorhadmadesomeefforttowardsthisgoalbyaddressingdirectlytheso-
lutionmethodsforvariousbranchesinmathematicsinasinglebook.Suchabook,
entitled“MATLABbasedsolutionstoadvancedappliedmathematics”,waspublished
firstin2004byTsinghuaUniversityPress.Severalneweditionsarepublishedafter-
wards:in2015,thesecondeditioninEnglishbyCRCPress,andin2018,thefourth
editioninChinesewerepublished.BasedonthelatestChineseedition,abrandnew
MOOCprojectwasreleasedin2018,1 andreceivedsignificantattention.Thenumber
of the registered students was about 14000 in the first round of the MOOC course,
andreachedtensofthousandsinlaterrounds.Thetextbookhasbeencitedtensof
thousandstimesbyjournalpapers,books,anddegreetheses.
Theauthorhasover30yearsofextensiveexperienceofusingMATLABinscientific
researchandeducation.Significantamountofmaterialsandfirst-handknowledgehas
beenaccumulated,whichcannotbecoveredinasinglebook.Aseriesentitled“Profes-
sorXueDingyü’sLectureHall”ofsuchworksarescheduledwithTsinghuaUniversity
Press,andtheEnglisheditionsareincludedintheDGSTEMserieswithDeGruyter.
Thesebooksareintendedtoprovidesystematic,extensiveanddeepexplorationsin
scientificcomputingskillswiththeuseofMATLABandrelatedtools.Theauthorwants
toexpresshissinceregratitudetohissupervisor,ProfessorDerekAthertonofSussex
University,whofirstbroughthimintotheparadiseofMATLAB.
ThisMATLABseriesisnotasimplerevisionoftheexistingbooks.Withdecadesof
experienceandmaterialaccumulation,theideaof“revisiting”isadoptedinauthor-
ingthesebooks,incontrasttoothermathematicsandotherMATLAB-richbooks.The
viewpointofanengineeringprofessorisestablishedandthefocusisonsolvingvar-
iousappliedmathematicalproblemswithtools.Manyinnovativeskillsandgeneral-
purposesolversareprovidedtosolveproblemswithMATLAB,whichisnotpossible
byanyotherexistingsolvers,soastobetterillustratetheapplicationsofcomputer
toolsinsolvingmathematicalproblemsineverymathematicsbranch.Italsohelps
1 MOOC(inChinese)address:https://www.icourse163.org/learn/NEU-1002660001
https://doi.org/10.1515/9783110666953-201
VI | Preface
thereadersbroadentheirviewpointsinscientificcomputing,andeveninfindingin-
novativesolutionsbythemselvestoscientificcomputingwhichcannotbesolvedby
anyotherexistingmethods.
ThefirsttitleintheMATLABseriescanbeusedasanentry-leveltextbookorrefer-
encebooktoMATLABprogramming,soastoestablishasolidfoundationanddeepun-
derstandingfortheapplicationofMATLABinscientificcomputing.Eachsubsequent
volumetriestocoverabranchortopicinmathematicalcourses.TheseMATLABbooks
aresuitableforthereaderswhohavealreadylearnttherelatedmathematicalcourses,
andrevisitthecoursestolearnhowtosolvetheproblemsbyusingcomputertools.
Itcanalsobeusedasacompanioninsynchronizingthelearningofrelatedmathe-
maticscourses,andforviewingthecoursefromadifferentangle.Thereadersmay
expandtheirknowledgeinlearningtherelatedcourses,soastobetterunderstand
andpracticetherelevantmaterials.Bearinginmindthe“computationalthinking”in
authoringtheseries,deepunderstandingandexplorationsaremadeforeachmathe-
maticsbranchinvolved.
ThisbookisthefirstintheMATLABseries.SystematicillustrationofMATLABpro-
grammingisprovidedinthebook.Thecommonlyuseddataandstatementstructures
inMATLABareintroducedfirst,followedbyalgebraicandtranscendentalfunction
evaluationsofmatrices,anddatamanipulations.Flowcontrolsandapplicationsin
MATLABprogrammingarethenintroduced,andMATLABfunctionprogrammingand
skillsareprovided.ScientificvisualizationinMATLABareaddressed.Advancedtop-
icssuchasthedesignsofMATLABinterfacetootherlanguages,object-orientedpro-
grammingandgraphicaluserinterfaceareillustrated,suchthatabetterfoundation
canbeestablishedforthereaderstocontinuelearningscientificcomputingandthe
knowledgeofotherrelatedmathematicalfields.
Atthetimethebooksarepublished,theauthorwishestoexpresshissinceregrat-
itudetohiswife,ProfessorYangJun.Herloveandselflesscareoverthedecadespro-
vided the author immense power, which supports his academic research, teaching
andwriting.
September2019 XueDingyü
Contents
Preface|V
1 Introductiontocomputermathematicslanguages|1
1.1 Introductiontosolvingmathematicalproblems|1
1.1.1 Whylearnacomputermathematicslanguage?|1
1.1.2 Analyticalandnumericalsolutions|5
1.1.3 Developmentofmathematicalpackages|6
1.1.4 Limitationsofconventionalcomputerlanguages|8
1.2 Historyofcomputermathematicslanguages|10
1.2.1 Theearlydaysofcomputermathematicslanguages|10
1.2.2 Representativemoderncomputermathematicslanguages|11
1.3 Three-phasesolutionofscientificcomputingproblems|12
1.4 Problems|14
2 FundamentalsofMATLABprogramming|17
2.1 Commandwindowsandfundamentalcommands|18
2.1.1 Regulationsinvariablenames|18
2.1.2 Reservedconstants|19
2.1.3 Settingofdisplayformats|20
2.1.4 Low-leveloperatingsystemcommands|21
2.1.5 SettingofMATLABworkingenvironment|21
2.1.6 MATLABworkspaceandmanagement|23
2.1.7 Othersupportingfacilities|23
2.2 Commonlyuseddatatypes|24
2.2.1 Numericdatatypes|24
2.2.2 Symbolicdata|26
2.2.3 Generationofarbitrarysymbolicmatrices|28
2.2.4 Symbolicfunctions|29
2.2.5 Integerandlogicvariables|29
2.2.6 Recognitionofdatatypes|29
2.2.7 Sizesandlengthsofmatrices|30
2.3 Stringdatatype|30
2.3.1 Expressionofstringvariables|30
2.3.2 Stringprocessingmethods|32
2.3.3 Conversionofstringvariables|33
2.3.4 Executionsofstringcommands|34
2.3.5 InterfaceofMuPADlanguage|35
2.4 Othercommonlyuseddatatypes|36
2.4.1 Multidimensionalarrays|36
2.4.2 Cellarrays|37
VIII | Contents
2.4.3 Tables|38
2.4.4 Structuredvariables|41
2.4.5 Otherdatatypes|42
2.5 Fundamentalstatementstructures|42
2.5.1 Directassignmentstatements|42
2.5.2 Functioncallstatements|43
2.5.3 Functionswithdifferentsyntaxes|43
2.5.4 Colonexpressions|44
2.5.5 Submatrixextractions|45
2.5.6 Generationofequallyspacedrowvectors|46
2.6 Readingandwritingofdifferentdatatypes|46
2.6.1 Readingandwritingofdatafiles|46
2.6.2 Low-levelreadingandwritingcommands|47
2.6.3 ReadingandwritingofExcelfiles|48
2.7 Problems|50
3 Fundamentalmathematicalcomputations|53
3.1 Algebraiccomputationofmatrices|53
3.1.1 Transposing,flippingandrotatingmatrices|53
3.1.2 Arithmeticoperations|55
3.1.3 Complexmatricesandtransformations|56
3.1.4 Powersandrootsofmatrices|57
3.1.5 Dotoperations|59
3.2 Logicandcomparisonoperations|59
3.2.1 Logicoperationswithmatrices|59
3.2.2 Comparisonsofmatrices|60
3.2.3 Searchingcommandsinmatrixelements|60
3.2.4 Attributejudgement|62
3.3 Computationoftranscendentalfunctions|62
3.3.1 Exponentialsandlogarithmicfunctions|63
3.3.2 Trigonometricfunctions|63
3.3.3 Inversetrigonometricfunctions|65
3.3.4 Transcendentalfunctionsofmatrices|66
3.4 Simplificationsandconversionsofsymbolicexpressions|68
3.4.1 Polynomialoperations|68
3.4.2 Conversionsandsimplificationsoftrigonometricfunctions|69
3.4.3 Simplificationofsymbolicexpressions|70
3.4.4 Variablesubstitutionofsymbolicexpressions|71
3.4.5 Conversionsofsymbolicexpressions|72
3.5 Fundamentalcomputationswithdata|72
3.5.1 Integerroundingandrationalizationofdata|73
3.5.2 Sortingandfindingmaximumandminimumofvectors|74
Contents | IX
3.5.3 Mean,varianceandstandarddeviation|75
3.5.4 Primefactorsandpolynomials|76
3.5.5 Permutationsandcombinations|78
3.6 Problems|79
4 FlowcontrolstructuresofMATLABlanguage|83
4.1 Loopstructures|83
4.1.1 Theforloopstructure|83
4.1.2 Thewhileloopstructure|86
4.1.3 Loopimplementationofiterations|87
4.1.4 Assistantstatementsofloopstructures|90
4.1.5 Vectorizedimplementationofloops|90
4.2 Conditionalstructures|93
4.2.1 Simpleconditionalstructures|93
4.2.2 Generalformofconditionalstructures|94
4.2.3 Vectorizedexpressionsofpiecewisefunctions|96
4.3 Switchstructures|98
4.4 Trialstructure|100
4.5 Problems|101
5 Functionprogramminganddebugging|105
5.1 MATLABscripts|105
5.2 FundamentalstructuresofMATLABfunctions|106
5.2.1 Fundamentalfunctionstructures|106
5.2.2 Regulationsinfunctionnames|108
5.2.3 Examplesoffunctionprogramming|108
5.3 SkillsofMATLABfunctionprogramming|112
5.3.1 Recursivestructures|112
5.3.2 Functionswithvariablenumbersofinputsandoutputs|114
5.3.3 Faulttolerancemanipulation|116
5.3.4 Globalvariables|117
5.3.5 ReadingandwritingofMATLABworkspace|118
5.3.6 Anonymousandinlinefunctions|119
5.3.7 Subfunctionsandprivatefunctions|121
5.4 MATLABfunctiondebugging|122
5.4.1 DebuggingofMATLABfunctions|122
5.4.2 Pseudocodeandcodeprotection|125
5.5 MATLABliveeditor|125
5.5.1 Liveeditorinterface|126
5.5.2 Creatingalivedocument|126
5.5.3 Executionofembeddedcode|128
5.5.4 Embedotherobjectsinliveeditor|128