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1、IntroductiontoTensorCalculusandContinuumMechanicsbyJ.H.HeinbockelDepartmentofMathematicsandStatisticsOldDominionUniversityPREFACEThisisanintroductorytextwhichpresentsfundamentalconceptsfromthesubjectareasoftensorcalculus,di?erentialgeometryandcontinuummechanics.Thematerialpresentedissuitabl
2、eforatwosemestercourseinappliedmathematicsandis?exibleenoughtobepresentedtoeitherupperlevelundergraduateorbeginninggraduatestudentsmajoringinappliedmathematics,engineeringorphysics.Thepresentationassumesthestudentshavesomeknowledgefromtheareasofmatrixtheory,linearalgebraandadvancedcalculus.
3、Eachsectionincludesmanyillustrativeworkedexamples.Attheendofeachsectionthereisalargecollectionofexerciseswhichrangeindi?culty.Manynewideasarepresentedintheexercisesandsothestudentsshouldbeencouragedtoreadalltheexercises.Thepurposeofpreparingthesenotesistocondenseintoanintroductorytextthebas
4、icde?nitionsandtechniquesarisingintensorcalculus,di?erentialgeometryandcontinuummechanics.Inparticular,thematerialispresentedto(i)developaphysicalunderstandingofthemathematicalconceptsassociatedwithtensorcalculusand(ii)developthebasicequationsoftensorcalculus,di?erentialgeometryandcontinuum
5、mechanicswhichariseinengineeringapplications.Fromthesebasicequationsonecangoontodevelopmoresophisticatedmodelsofappliedmathematics.Thematerialispresentedinaninformalmannerandusesmathematicswhichminimizesexcessiveformalism.Thematerialhasbeendividedintotwoparts.The?rstpartdealswithanintroduc-
6、tiontotensorcalculusanddi?erentialgeometrywhichcoverssuchthingsastheindicialnotation,tensoralgebra,covariantdi?erentiation,dualtensors,bilinearandmultilinearforms,specialtensors,theRiemannChristo?eltensor,spacecurves,surfacecurves,cur-vatureandfundamentalquadraticforms.Thesecondpartemphasiz
7、estheapplicationoftensoralgebraandcalculustoawidevarietyofappliedareasfromengineeringandphysics.Theselectedapplicationsarefromtheareasofdynamics,elasticity,?uidsandelectromag-netictheory.Thecontinuummechanicsportionfocusesonanintroductionofthebasicconcep
