高等数学（上 英文版）/高等院校双语教学规划教材

图书标准信息

• 作者 东南大学大学数学教研室 编
• 出版社 东南大学出版社
• 出版时间 2014-09
• 版次 1
• ISBN 9787564151737
• 定价 36.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 252页
• 字数 319千字
• 正文语种 简体中文，英语
• 丛书 高等院校双语教学规划教材

【内容简介】

　　《高等数学（上英文版）/高等院校双语教学规划教材》是为响应东南大学国际化需要，根据国家教育部非数学专业数学基础课教学指导分委员会制定的工科类本科数学基础课程教学基本要求，并结合东南大学数学系多年教学改革实践经验编写的全英文教材。
　　《高等数学（上英文版）/高等院校双语教学规划教材》分为上、下两册，内容包括极限、一元函数微分学、一元函数积分学、常微分方程、级数、向鼍代数与空间解析几何、多元函数微分学、多元函数积分学、向量场的积分、复变函数等十个章节。
　　《高等数学（上英文版）/高等院校双语教学规划教材》可作为高等理工科院校非数学类专业本科生学习高等数学的英文教材。也可供其他专业选用和社会读者阅读。

【目录】

Chapter1Limits
1.1TheConceptofLimitsanditsProperties
1.1.1LimitsofSequence
1.1.2LimitsofFunctions
1.1.3PropertiesofLimits
Exercise1.1
1.2LimitsTheorem
1.2.1RulesforFindingLimits
1.2.2TheSandwichTheorem
1.2.3MonotonicSequenceTheorem
1.2.4TheCauchyCriterion
Exercise1.2
1.3TwoImportantSpecialLimits
Exercise1.3
1.4InfinitesimalandInfinite
1.4.1Infinitesimal
1.4.2Infinite
Exercise1.4
1.5ContinuousFunction
1.5.1Continuity
1.5.2Discontinuity
Exercise1.5
1.6TheoremsaboutContinuousFunctiononaClosedInterval
Exercise1.6
ReviewandExercise

Chapter2Differentiation
2.1TheDerivative
Exercise2.1
2.2RulesforFingdingtheDerivative
2.2.1DerivativeofArithmeticCombination
2.2.2TheDerivativeRuleforInverses
2.2.3DerivativeofComposition
2.2.4ImplicitDifferentiation
2.2.5ParametricDifferentiation
2.2.6RelatedRatesofChange
Exercise2.2
2.3Higher-OrderDerivatives
Exercise2.3
2.4Differentials
Exercise2.4
2.5TheMeanValueTheorem
Exercise2.5
2.6L'Hospital'sRule
Exercise2.6
2.7Taylor'sTheorem
Exercise2.7
2.8ApplicationsofDerivatives
2.8.1Monotonicity
2.8.2LocalExtremeValues
2.8.3ExtremeValues
2.8.4Concavity
2.8.5GraphingFunctions
Exercise2.8
ReviewandExercise

Chapter3TheIntegration
3.1TheDefiniteIntegral
3.1.1TwoExamples
3.1.2TheDefinitionofDefiniteIntegral
3.1.3PropertiesofDefiniteIntegrals
Exercise3.1
3.2TheIndefiniteIntegral
Exercise3.2
3.3TheFundamentalTheorem
3.3.1FirstFundamentalTheorem
3.3.2SecondFundamentalTheorem
Exercise3.3
3.4TechniquesofIndefiniteIntegration
3.4.1SubstitutioninIndefiniteIntegrals
3.4.2IndefiniteIntegrationbyParts
3.4.3IndefiniteIntegrationofRationalFunctionsby
PartialFractions
Exercise3.4
3.5TechniquesofDefiniteIntegration
3.5.1SubstitutioninDefiniteIntegrals
3.5.2DefiniteIntegrationbyParts
Exercise3.5
3.6ApplicationsofDefiniteIntegrals
3.6.1LengthsofPlaneCurves
3.6.2AreabetweenTwoCurves
3.6.3VolumesofSolids
3.6.4AreasofSurfaceofRevolution
3.6.5MomentsandCenterofMass
3.6.6WorkandFluidForce
Exercise3.6
3.7ImproperIntegrals
3.7.1ImproperIntegrals.InfiniteLimitsofIntegration
3.7.2ImproperIntegrals：InfiniteIntegrands
Exercise3.7
ReviewandExercise

Chapter4DifferentialEquations
4.1TheConceptofDifferentialEquations
Exercise4.1
4.2DifferentialEquationsoftheFirstOrder
4.2.1EquationswithVariableSeparable
4.2.2HomogeneousEquation
Exercise4.2
4.3First-orderLinearDifferentialEquations
Exercise4.3
4.4EquationsReducibletoFirstOrder
4.4.1EquationsoftheFormy（n）=f（x）
4.4，2EquationsoftheFormy=y（x，y）
4.4.3EquationsoftheFormy=f（y，y'）
Exercise4.4
4.5LinearDifferentialEquations
4.5.1BasicTheoryofLinearDifferentialEquations
4.5.2HomogeneousLinearDifferentialEquationsofthe
SecondOrderwithConstantCoefficients
4.5.3NonhomogeneousLinearDifferentialEquationsofthe
SecondOrderwithConstantCoefficients
4.5.4EulerDifferentialEquation
Exercise4.5
4.6SystemsofLinearDifferentialEquations
withConstantCoefficients
Exercise4.6
4.7Applications
Exercise4.7
ReviewandExercise