[Michael_Spivak]_Calculus_on_Manifolds_A_Modern

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1、MichaelSpivakBrandeisUniversityCalculusonManifoldsAMODERNAPPROACHTOCLASSICALTHEOREMSOFADVANCEDCALCULUSADDISON-WESLEYPUBLISHINGCOMPANYTheAdvancedBookProgramReading,Massachusetts•MenloPark,California•NewYorkDonMills,Ontario•Wokingham,England•Amsterdam•Bonn

2、Sydney•Singapore•Tokyo•Madrid•SanJuan•ParisSeoul•Milan•MexicoCity•TaipeiCalculusonManifoldsAModemApproachtoClassicalTheoremsofAdvancedCalculusCopyright©1965byAddison-WesleyPublishingCompanyAllrightsreservedLibraryofCongressCardCatalogNumber66-10910Manufa

3、cturedintheUnitedStatesofAmericaThemanuscriptwasputintoproductiononApril21,1965;thisvolumewaspublishedonOctober26,1965ISBN0-8053-9021-92425262728-CRW-9998979695Twenty-fourthprinting,January1995Editors'ForewordMathematicshasbeenexpandinginalldirectionsata

4、fabulousrateduringthepasthalfcentury.Newfieldshaveemerged,thediffusionintootherdisciplineshasproceededapace,andourknowledgeoftheclassicalareashasgrownevermoreprofound.Atthesametime,oneofthemoststrikingtrendsinmodernmathematicsistheconstantlyincreasingint

5、errelationshipbetweenitsvariousbranches.Thusthepresent-daystudentsofmathematicsarefacedwithanimmensemountainofmaterial.Inadditiontothetraditionalareasofmathematicsaspresentedinthetraditionalmanner-andthesepresentationsdoabound-therearethenewandoftenenlig

6、hteningwaysoflookingatthesetraditionalareas,andalsothevastnewareasteemingwithpotentialities.Muchofthisnewmaterialisscatteredindigestiblythroughouttheresearchjournals,andfrequentlycoherentlyorganizedonlyinthemindsorunpublishednotesoftheworkingmathematicia

7、ns.Andstudentsdesperatelyneedtolearnmoreandmoreofthismaterial.ThisseriesofbrieftopicalbookletshasbeenconceivedasapossiblemeanstotackleandhopefullytoalleviatesomeofvviEditors'Forewordthesepedagogicalproblems.Theyarebeingwrittenbyactiveresearchmathematicia

8、ns,whocanlookatthelatestdevelopments,whocanusethesedevelopmentstoclarifyandcondensetherequiredmaterial,whoknowwhatideastounderscoreandwhattechniquestostress.Wehopethattheywillalsoservetopresenttotheableundergraduateanintro