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1、AnIntroductiontoMultivariableMathematicsCopyright©2008byMorgan&ClaypoolAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans—electronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotationsinprintedrevi
2、ews,withoutthepriorpermissionofthepublisher.AnIntroductiontoMultivariableMathematicsLeonSimonwww.morganclaypool.comISBN:9781598298017paperbackISBN:9781598298024ebookDOI10.2200/S00147ED1V01Y200808MAS003APublicationintheMorgan&ClaypoolPublishersseriesSYNTHESISLECTURESONMATHEMATI
3、CSANDSTATISTICSLecture#3SeriesEditor:StevenG.Krantz,WashingtonUniversity,St.LouisSeriesISSNSynthesisLecturesonMathematicsandStatisticsISSNpending.AnIntroductiontoMultivariableMathematicsLeonSimonStanfordUniversitySYNTHESISLECTURESONMATHEMATICSANDSTATISTICS#3MMorgan&cLaypoolpub
4、lishers&CABSTRACTThetextisdesignedforuseina40lectureintroductorycoursecoveringlinearalgebra,multivariabledifferentialcalculus,andanintroductiontorealanalysis.Thecorematerialofthebookisarrangedtoallowforthemainintroductorymaterialonlinearalgebra,includingbasicvectorspacetheoryi
5、nEuclideanspaceandtheinitialtheoryofmatricesandlinearsystems,tobecoveredinthefirst10or11lectures,followedbyasimilarnumberoflecturesonbasicmultivariableanalysis,includingfirsttheoremsondifferentiablefunctionsondomainsinEuclideanspaceandabriefintroductiontosubmanifolds.Thebookthen
6、concludeswithfurtheressentiallinearalgebra,includingthetheoryofdeterminants,eigenvalues,andthespectraltheoremforrealsymmetricmatrices,andfurthermultivariableanalysis,includingthecontractionmappingprincipleandtheinverseandimplicitfunctiontheorems.Thereisalsoanappendixwhichprovi
7、desa9lectureintroductiontorealanalysis.Therearevariouswaysinwhichtheadditionalmaterialintheappendixcouldbeintegratedintoacourse—forexampleintheStanfordMathematicshonorsprogram,runasa4lectureperweekprogramintheAutumnQuartereachyear,thefirst6lecturesofthe9lectureappendixarepresen
8、tedattherateofonelectureaweekinweeks2–7ofthequarter,withthere