Vector Analysis.pdf

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1、VectoranalysisAphysicist'sguidetothemathematicsoffieldsinthreedimensionsVectoranalysisAphysicist'sguidetothemathematicsoffieldsinthreedimensionsN.KEMMERTaitProfessorofMathematicalPhysicsUniversityofEdinburghCAMBRIDGEUNIVERSITYPRESSCAMBRIDGELONDONNEWYORKMELBOU

2、RNECAMBRIDGEUNIVERSITYPRESSCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SaoPaulo,DelhiCambridgeUniversityPressTheEdinburghBuilding,CambridgeC1328RU,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationont

3、histitle:www.cambridge.org/9780521211581©CambridgeUniversityPress1977Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUni

4、versityPress.Firstpublished1977Re-issuedinthisdigitallyprintedversion2008AcataloguerecordforthispublicationisavailablefromtheBritishLibraryLibraryofCongressCatalogueCardNumber:75-36025ISBN978-0-521-21158-1hardbackISBN978-0-521-29064-7paperbackContentsPrefacep

5、ageixIntroductionxi1Summaryofvectoralgebra1Additionandmultiplicationofvectors12Thecartesiancomponentsofavector53Thequotienttheorem7ExercisesA92Thegeometricalbackgroundtovectoranalysis1Thepoint132Thecurve133Thesurface174Thethree-dimensionalregionofspace223Metr

6、icpropertiesofEuclideanspace1Thelengthofacurveandthetotalmassonit272Theareaofasurfaceandthetotalmassonit283Thevolumeof,andmassinathree-dimensional29regionExercisesB314Scalarandvectorfields1Scalarfields372Vectorfields40ExercisesC455Spatialintegralsoffields1The

7、workintegral492Thefluxintegral543Thequantityintegral58vContents6Furtherspatialintegrals1Vectorintegrals602Moregeneralintegralsoverfields65ExercisesD677Differentiationoffields.Part1:thegradient1TheoperatorV722Thegradientofascalarfield733Thefieldlinepictureofag

8、radientfield744Analternativedefinitionofgrad0775Thefundamentalpropertyofagradientfield788Differentiationoffields.Part2:thecurl1Definitionofthecurlofavectorfield812Evaluationofcurlf.Stokes