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1、IntroductiontoTensorCalculusandContinuumMechanicsbyJ.H.HeinbockelDepartmentofMathematicsandStatisticsOldDominionUniversityPREFACEThisisanintroductorytextwhichpresentsfundamentalconceptsfromthesubjectareasoftensorcalculus,differentialgeometryandcontinuum
2、mechanics.Thematerialpresentedissuitableforatwosemestercourseinappliedmathematicsandisflexibleenoughtobepresentedtoeitherupperlevelundergraduateorbeginninggraduatestudentsmajoringinappliedmathematics,engineeringorphysics.Thepresentationassumesthestudent
3、shavesomeknowledgefromtheareasofmatrixtheory,linearalgebraandadvancedcalculus.Eachsectionincludesmanyillustrativeworkedexamples.Attheendofeachsectionthereisalargecollectionofexerciseswhichrangeindifficulty.Manynewideasarepresentedintheexercisesandsothest
4、udentsshouldbeencouragedtoreadalltheexercises.Thepurposeofpreparingthesenotesistocondenseintoanintroductorytextthebasicdefinitionsandtechniquesarisingintensorcalculus,differentialgeometryandcontinuummechanics.Inparticular,thematerialispresentedto(i)devel
5、opaphysicalunderstandingofthemathematicalconceptsassociatedwithtensorcalculusand(ii)developthebasicequationsoftensorcalculus,differentialgeometryandcontinuummechanicswhichariseinengineeringapplications.Fromthesebasicequationsonecangoontodevelopmoresophi
6、sticatedmodelsofappliedmathematics.Thematerialispresentedinaninformalmannerandusesmathematicswhichminimizesexcessiveformalism.Thematerialhasbeendividedintotwoparts.Thefirstpartdealswithanintroduc-tiontotensorcalculusanddifferentialgeometrywhichcoverssuch
7、thingsastheindicialnotation,tensoralgebra,covariantdifferentiation,dualtensors,bilinearandmultilinearforms,specialtensors,theRiemannChristoffeltensor,spacecurves,surfacecurves,cur-vatureandfundamentalquadraticforms.Thesecondpartemphasizestheapplicationof
8、tensoralgebraandcalculustoawidevarietyofappliedareasfromengineeringandphysics.Theselectedapplicationsarefromtheareasofdynamics,elasticity,fluidsandelectromag-netictheory.Thecontinuummechanicsportionfocusesonanintroductionofthebasicconcep
