数学分析课程英文描述.doc

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1、MathematicalAnalysis(FirstVolumeandSecondVolume)EditedbyMathematicalAnalysiscoursegroup,DepartmentofMathematics,ShanghaiJiaoTongUniversityPublishedbyHigherEducationPressMaterialcovered:A.AggregatesandfunctionsB.Limitsandcontinuity1)Serieslimit2)Functionslimit3)Functionsco

2、ntinuity4)Heine–BorelTheoremandBolzano-WeierstrassTheoremC.Differentialcalculusandderivative1)Definitionandalgorithmofderivative2)Differentialcalculus3)Higher-orderderivativeD.DifferentialMeanValueTheorem1)LagrangeMeanValueTheorem2)L’HospitalRule3)Taylor’sformula4)Jensen’

3、sinequalityE.IndefiniteintegralF.Definiteintegral1)FirstIntegrationMid-valueTheorem2)Newton-LeibnitzFormula3)SecondIntegrationMid-valueTheoremandRiemannLemmaG.ImproperintegralH.InfiniteSeries1)Limitsuperiorandlimitinferiorofareal-valuedsequence2)Cauchy’sconditionforconver

4、genceofseries3)Absoluteandconditionalconvergence4)Varioustestsforseries5)Dirichlet’stestandAbel’stest I.SeriesofFunctions1)Uniformconvergence2)Cauchy’sconditionforuniformconvergence3)Dirichlet’stest,Abel’stestandWeierstrass’stestforuniformconvergence4)MeanconvergenceJ.Pow

5、erseriesK.LimitsandcontinuityofmultivariatefunctionsandtheEuclidSpaceL.MultivariableDifferentialCalculus1)Partialderivative2)Totalderivative3)Thechainrule4)Higher-orderpartialderivativeandtotalderivative5)Implicitfunctionexistencetheorem6)DirectionalderivativeandgradientM

6、.Multipleintegral1)Doubleintegral2)TripleintegralN.Lineintegralandsurfaceintegral