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1、IntroductiontoTensorCalculusandContinuumMechanicsbyJ.H.HeinbockelDepartmentofMathematicsandStatisticsOldDominionUniversityPREFACEThisisanintroductorytextwhichpresentsfundamentalconceptsfromthesubjectareasoftensorcalculus,differentialgeometryandcontinuumm
2、echanics.Thematerialpresentedissuitableforatwosemestercourseinappliedmathematicsandisflexibleenoughtobepresentedtoeitherupperlevelundergraduateorbeginninggraduatestudentsmajoringinappliedmathematics,engineeringorphysics.Thepresentationassumesthestudentsh
3、avesomeknowledgefromtheareasofmatrixtheory,linearalgebraandadvancedcalculus.Eachsectionincludesmanyillustrativeworkedexamples.Attheendofeachsectionthereisalargecollectionofexerciseswhichrangeindifficulty.Manynewideasarepresentedintheexercisesandsothestude
4、ntsshouldbeencouragedtoreadalltheexercises.Thepurposeofpreparingthesenotesistocondenseintoanintroductorytextthebasicdefinitionsandtechniquesarisingintensorcalculus,differentialgeometryandcontinuummechanics.Inparticular,thematerialispresentedto(i)developap
5、hysicalunderstandingofthemathematicalconceptsassociatedwithtensorcalculusand(ii)developthebasicequationsoftensorcalculus,differentialgeometryandcontinuummechanicswhichariseinengineeringapplications.Fromthesebasicequationsonecangoontodevelopmoresophistica
6、tedmodelsofappliedmathematics.Thematerialispresentedinaninformalmannerandusesmathematicswhichminimizesexcessiveformalism.Thematerialhasbeendividedintotwoparts.Thefirstpartdealswithanintroduc-tiontotensorcalculusanddifferentialgeometrywhichcoverssuchthings
7、astheindicialnotation,tensoralgebra,covariantdifferentiation,dualtensors,bilinearandmultilinearforms,specialtensors,theRiemannChristoffeltensor,spacecurves,surfacecurves,cur-vatureandfundamentalquadraticforms.Thesecondpartemphasizestheapplicationoftensora
8、lgebraandcalculustoawidevarietyofappliedareasfromengineeringandphysics.Theselectedapplicationsarefromtheareasofdynamics,elasticity,fluidsandelectromag-netictheory.Thecontinuummechanicsportionfocusesonanintroductionofthebasicconcep
