Intro to Tensor Calculus

Intro to Tensor Calculus

ID:34656429

大小:3.34 MB

页数:373页

时间:2019-03-08

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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

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