Introduction_to_Vectors_and_Tensors

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1、INTRODUCTIONTOVECTORSANDTENSORSLinearandMultilinearAlgebraVolume1RayM.BowenMechanicalEngineeringTexasA&MUniversityCollegeStation,TexasandC.-C.WangMathematicalSciencesRiceUniversityHouston,TexasCopyrightRayM.BowenandC.-C.Wang(ISBN0-306-37508-7(v.1))________________________________

2、____________________________________________PREFACEToVolume1Thisworkrepresentsourefforttopresentthebasicconceptsofvectorandtensoranalysis.VolumeIbeginswithabriefdiscussionofalgebraicstructuresfollowedbyaratherdetaileddiscussionofthealgebraofvectorsandtensors.VolumeIIbeginswithadi

3、scussionofEuclideanManifoldswhichleadstoadevelopmentoftheanalyticalandgeometricalaspectsofvectorandtensorfields.adiscussionofgeneraldifferentiablemanifolds.Wehavenotincludedadiscussionofgeneraldifferentiablemanifolds.However,wehaveincludedachapteronvectorandtensorfieldsdefinedonH

4、ypersurfacesinaEuclideanManifold.InpreparingthistwovolumeworkourintentionistopresenttoEngineeringandSciencestudentsamodernintroductiontovectorsandtensors.Traditionalcoursesonappliedmathematicshaveemphasizedproblemsolvingtechniquesratherthanthesystematicdevelopmentofconcepts.Asare

5、sult,itispossibleforsuchcoursestobecometerminalmathematicscoursesratherthancourseswhichequipthestudenttodevelophisorherunderstandingfurther.AsEngineeringstudentsourcoursesonvectorsandtensorsweretaughtinthetraditionalway.Welearnedtoidentifyvectorsandtensorsbyformaltransformationru

6、lesratherthanbytheircommonmathematicalstructure.Thesubjectseemedtoconsistofnothingbutacollectionofmathematicalmanipulationsoflongequationsdecoratedbyamultitudeofsubscriptsandsuperscripts.Priortoourapplyingvectorandtensoranalysistoourresearchareaofmoderncontinuummechanics,wealmost

7、hadtorelearnthesubject.Therefore,oneofourobjectivesinwritingthisbookistomakeavailableamodernintroductorytextbooksuitableforthefirstin-depthexposuretovectorsandtensors.Becauseofourinterestinapplications,itisourhopethatthisbookwillaidstudentsintheireffortstousevectorsandtensorsinap

8、pliedareas.Thepresentationofthebasicmath