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1、DavidBachmanAGeometricApproachtoDifferentialFormsSecondEditionDavidBachmanPitzerCollegeDepartmentofMathematics1050N.MillsAvenueClaremont,CA91711USAbachman@pitzer.eduISBN978-0-8176-8303-0e-ISBN978-0-8176-8304-7DOI10.1007/978-0-8176-8304-7SpringerNewYorkDordre
2、chtHeidelbergLondonLibraryofCongressControlNumber:2011940222MathematicsSubjectClassification(2010):53-01,53A04,53A05,53A45,53B21,58A10,58A12,58A15©SpringerScience+BusinessMedia,LLC2006,2012Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwi
3、thoutthewrittenpermissionofthepublisher(BirkhäuserBoston,c/oSpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,ele
4、ctronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionast
5、owhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperBirkhäuserBostonispartofSpringerScience+BusinessMedia(www.birkhauser.com)PrefacetotheSecondEditionTheoriginaleditionofthisbookwaswrittentobeaccessibletosophomore-levelundergraduates,whohad
6、onlyseenoneyearofastandardcalculusse-quence.Inparticular,formostofthetext,nopriorexposuretomultivariablecalculus,vectorcalculus,orlinearalgebrawasassumed.Afterreceivinglotsofreaderfeedbacktothefirstedition,itbecameclearthatthepeoplereadingthisbookweremoreadva
7、nced.Hence,forthesecondedition,mostofthematerialonbasictopicssuchaspartialderivativesandmultipleintegralshasbeenremoved,andmoreadvancedapplicationsofdifferentialformshavebeenadded.Thelargestofthenewadditionsisachaptercontaininganintroductiontodifferentialgeome
8、try,basedonthemachineryofdifferentialforms.Atalltimes,wehavemadeanefforttobeconsistentwiththerestofthetexthere,sothatthematerialispresentedinR3forconcreteness,butalldefinitionsareformulatedtoeasily
