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1、IntroductiontoTensorCalculusandContinuumMechanicsbyJ.H.HeinbockelDepartmentofMathematicsandStatisticsOldDominionUniversityPREFACEThisisanintroductorytextwhichpresentsfundamentalconceptsfromthesubjectareasoftensorcalculus,di erentialgeometryandcontinuummechanics.Thematerialpresentedissuitableforatwos
2、emestercourseinappliedmathematicsandis?exibleenoughtobepresentedtoeitherupperlevelundergraduateorbeginninggraduatestudentsmajoringinappliedmathematics,engineeringorphysics.Thepresentationassumesthestudentshavesomeknowledgefromtheareasofmatrixtheory,linearalgebraandadvancedcalculus.Eachsectioninclude
3、smanyillustrativeworkedexamples.Attheendofeachsectionthereisalargecollectionofexerciseswhichrangeindiculty.Manynewideasarepresentedintheexercisesandsothestudentsshouldbeencouragedtoreadalltheexercises.Thepurposeofpreparingthesenotesistocondenseintoanintroductorytextthebasicde nitionsandtechniquesar
4、isingintensorcalculus,di erentialgeometryandcontinuummechanics.Inparticular,thematerialispresentedto(i)developaphysicalunderstandingofthemathematicalconceptsassociatedwithtensorcalculusand(ii)developthebasicequationsoftensorcalculus,di erentialgeometryandcontinuummechanicswhichariseinengineeringappl
5、ications.Fromthesebasicequationsonecangoontodevelopmoresophisticatedmodelsofappliedmathematics.Thematerialispresentedinaninformalmannerandusesmathematicswhichminimizesexcessiveformalism.Thematerialhasbeendividedintotwoparts.The rstpartdealswithanintroduc-tiontotensorcalculusanddi erentialgeometrywhi
6、chcoverssuchthingsastheindicialnotation,tensoralgebra,covariantdi erentiation,dualtensors,bilinearandmultilinearforms,specialtensors,theRiemannChristo eltensor,spacecurves,surfacecurves,cur-vatureandfundamentalquadraticforms.Thesecondpartemphasizestheapplicationoftensoralgebraandcalculustoawidevarie
7、tyofappliedareasfromengineeringandphysics.Theselectedapplicationsarefromtheareasofdynamics,elasticity,?uidsandelectromag-netictheory.Thecontinuummechanicsportionfocusesonanintroductionofthebasicconcep
