資源描述：
《Tensor Analysis on Manifolds英文學(xué)習(xí)資料》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、TensorAnalysisonManifoldsRichardL.BishopUniversityofIllinoisSamuelI.GoldbergUniversityofIllinoisBig"'_cmtraleFacjliaInyagneria0G0312DoverPublications,Inc.NewYorkCopyright?1968,1980byRichardLBishopandSamuelIGoldbergAllrightsreservedunderPanAmericanandInternationa
2、lCopyrightConventionsThisDoveredition,firstpublishedin1980,isanunabridg(andcorrectedrepublicationoftheworkoriginallypublishibyTheMacmillanCompanyin1968InternationalStandardBookNumber0-486-64039-6LibraryofCongressCatalogCardNumber80-66959ManufacturedintheUnitedSt
3、atesofAmericaDoverPublications,Inc31East2ndStreet,Mineola,N.Y.11501Preface"SiebedeuteteinenwahrenTriumphderdurchGauss,Riemann,Christoffel,Ricci...begrundetenMethodendesallgemeinenDifferentialcalculus."ALBERTEINSTEIN,1915SINCEITSDEVELOPMENTBYRiccibetween1887and18
4、96,tensoranalysishashadaratherrestrictedoutlookdespiteitsstrikingsuccessasamathematicaltoolinthegeneraltheoryofrelativityanditsadaptabilitytoawiderangeofproblemsindifferentialequations,geometry,andphysics.Theemphasishasbeenonnotationandmanipulationofindices.This
5、bookisanattempttobroadenthispointofviewatthestagewherethestudentfirstencountersthesubject.Wehavetreatedtensoranalysisasacontinuationofadvancedcalcu-lus,andourstandardsofrigorandlogicalcompletenesscomparefavorablywithparallelcoursesinthecurriculumsuchascomplexvar
6、iabletheoryandlinearalgebra.Forstudentsinthephysicalsciences,whoacquiremathematicalknowledgeona"need-to-know"basis,thisbookprovidesorganization.Ontheotherhand,itcanbeusedbymathematicsstudentsasameaningfulintroductiontodifferentialgeometry.Abroadrangeofnotationsi
7、sexplainedandinterrelated,sothestudentwillbeabletocontinuehisstudiesamongeithertheclassicalreferences,thoseinthestyleofE.Cartan,orthecurrentabstractions.Thematerialhasbeenorganizedaccordingtothedictatesofmathematicalstructure,proceedingfromthegeneraltothespecial
8、.Theinitialchapterhasbeennumbered0becauseitlogicallyprecedesthemaintopics.ThusChapter0establishesnotationandgivesanoutlineofabodyoftheoryrequiredtoputtheremainingchap
