manifolds, tensor analysis and applications 3rd ed. - marsden, ratiu and abraham

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1、PageiManifolds,TensorAnalysis,andApplicationsThirdEditionJerroldE.MarsdenTudorRatiuControlandDynamicalSystems107–81D´epartementdeMath´ematiquesCaliforniaInstituteofTechnologyEcolepolytechniquefederaledeLausanne´Pasadena,California91125CH-1015Lausanne,Switzerlandwit

2、hthecollaborationofRalphAbrahamDepartmentofMathematicsUniversityofCalifornia,SantaCruzSantaCruz,California95064Thisversion:January5,2002iiLibraryofCongressCataloginginPublicationDataMarsden,JerroldManifolds,tensoranalysisandapplications,ThirdEdition(AppliedMathemat

3、icalSciences)Bibliography:p.631Includesindex.1.Globalanalysis(Mathematics)2.Manifolds(Mathematics)3.Calculusoftensors.I.Marsden,JerroldE.II.Ratiu,TudorS.III.Title.IV.Series.QA614.A281983514.382-1737ISBN0-201-10168-SAmericanMathematicsSociety(MOS)SubjectClassificatio

4、n(2000):34,37,58,70,76,93Copyright2001bySpringer-VerlagPublishingCompany,Inc.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortrans-mitted,inanyorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorw

5、rittenpermissionofthepublisher,Springer-VerlagPublishingCompany,Inc.,175FifthAvenue,NewYork,N.Y.10010.PageiContentsPrefaceiii1Topology11.1TopologicalSpaces.........................................11.2MetricSpaces............................................81.3Conti

6、nuity..............................................121.4Subspaces,Products,andQuotients...............................151.5Compactness............................................201.6Connectedness...........................................261.7BaireSpaces..........

7、...................................312BanachSpacesandDifferentialCalculus352.1BanachSpaces...........................................352.2LinearandMultilinearMappings.................................492.3TheDerivative...........................................662.4P

8、ropertiesoftheDerivative....................................722.5TheInverseandImplicitFunctionTheorems..........................1013ManifoldsandV