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1、DIFFERENTIALFORMSANDCONNECTIONSR.W.R.DARLINGThisbookintroducesthetoolsofmoderndifferentialgeometry-exteriorcalculus,manifolds,vectorbundles,connections-toadvancedundergraduatesandbeginninggraduatestudentsinmathematics,physics,andengineering.Itcoversbothclassicalsurfacetheoryandthemode
2、rntheoryofconnectionsandcurvature,andincludesachapteronapplicationstotheoreticalphysics.Theonlyprerequisitesaremultivariatecalculusandlinearalgebra;noknowledgeoftopologyisassumed.Thepowerfulandconcisecalculusofdifferentialformsisusedthroughout.Throughtheuseofnumerousconcreteexamples,t
3、heauthordevelopscomputationalskillsinthefamiliarEuclideancontextbeforeexposingthereadertothemoreabstractsettingofmanifolds.Therearenearly200exercises,makingthebookidealforbothclassroomuseandself-study.DifferentialFormsandConnectionsDifferentialFormsandConnectionsR.W.R.DarlingUniversit
4、yofSouthFloridaCAMBRIDGEUNIVERSITYPRESSPUBLISHEDBYTHEPRESSSYNDICATEOFTHEUNIVERSITYOFCAMBRIDGEThePittBuilding.TrumpingtonStreet,Cambridge,UnitedKingdomCAMBRIDGEUNIVERSITYPRESSTheEdinburghBuilding,CambridgeCB22RU,UKhttp://www.cup.cam.ac.uk40West20thStreet,NewYork,NY10011-4211,USAhttp://
5、www.cuporg10StamfordRoad,Oakleigh,Melbourne3166,AustraliaRuizdeAlarc6n13,28014Madrid,Spain®CambridgeUniversityPress1994Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermiss
6、ionofCambridgeUniversityPress.Firstpublished1994Reprinted1995,1996,1999PrintedintheUnitedStatesofAmericaAcatalogrecordforthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloginginPublicationDataisavailableISBN0521462592hardbackISBN0521468000paperbackContentsPrefaceix1Exteri
7、orAlgebra11.1ExteriorPowersofaVectorSpace11.2MultilinearAlternatingMapsandExteriorProducts51.1Exercises71.4ExteriorPowersofaLinearTransformation1.5Exercises21.6InnerProductsL1.7TheHodgeStarOperator171.8Exercises2B1.9SomeFormalAlgebraicConstructions211.10HistoryandBibliography232Exteri
8、orCal
