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1、IntroductiontoTensorCalculusandContinuumMechanicsbyJ.H.HeinbockelDepartmentofMathematicsandStatisticsOldDominionUniversityPREFACEThisisanintroductorytextwhichpresentsfundamentalconceptsfromthesubjectareasoftensorcalculus,di erentialgeometryandcontinuummech
2、anics.Thematerialpresentedissuitableforatwosemestercourseinappliedmathematicsandisflexibleenoughtobepresentedtoeitherupperlevelundergraduateorbeginninggraduatestudentsmajoringinappliedmathematics,engineeringorphysics.Thepresentationassumesthestudentshavesom
3、eknowledgefromtheareasofmatrixtheory,linearalgebraandadvancedcalculus.Eachsectionincludesmanyillustrativeworkedexamples.Attheendofeachsectionthereisalargecollectionofexerciseswhichrangeindiculty.Manynewideasarepresentedintheexercisesandsothestudentsshould
4、beencouragedtoreadalltheexercises.Thepurposeofpreparingthesenotesistocondenseintoanintroductorytextthebasicde nitionsandtechniquesarisingintensorcalculus,di erentialgeometryandcontinuummechanics.Inparticular,thematerialispresentedto(i)developaphysicalunder
5、standingofthemathematicalconceptsassociatedwithtensorcalculusand(ii)developthebasicequationsoftensorcalculus,di erentialgeometryandcontinuummechanicswhichariseinengineeringapplications.Fromthesebasicequationsonecangoontodevelopmoresophisticatedmodelsofappl
6、iedmathematics.Thematerialispresentedinaninformalmannerandusesmathematicswhichminimizesexcessiveformalism.Thematerialhasbeendividedintotwoparts.The rstpartdealswithanintroduc-tiontotensorcalculusanddi erentialgeometrywhichcoverssuchthingsastheindicialnotat
7、ion,tensoralgebra,covariantdi erentiation,dualtensors,bilinearandmultilinearforms,specialtensors,theRiemannChristo eltensor,spacecurves,surfacecurves,cur-vatureandfundamentalquadraticforms.Thesecondpartemphasizestheapplicationoftensoralgebraandcalculustoaw
8、idevarietyofappliedareasfromengineeringandphysics.Theselectedapplicationsarefromtheareasofdynamics,elasticity,fluidsandelectromag-netictheory.Thecontinuummechanicsportionfocusesonanintroductionofthebasicconcep
