高等数学(上)(英文版)
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北京东城
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作者东南大学大学数学教研室
出版社东南大学出版社
ISBN9787564151737
出版时间2014-09
装帧平装
开本16开
定价45元
货号1201946142
上书时间2024-12-20
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目录
Chapter 1 Limits
1.1 The Concept of Limits and its Properties
1.1.1 Limits of Sequence
1.1.2 Limits of Functions
1.1.3 Properties ofl.imits
Exercise 1.1
1.2 Limit.s Theorem
1.2.1 Rules for Finding Limits
1.2.2 The Sandwich Theorem
1.2.3 Monotonic Sequence Theorem
1.2.4 The Cauchy Criterion
Exercise 1.2
1.3 Twolmportant Spe Limits
Exercise 1.3
1.4 Infinitesimal and Infinite
1.4.1 Infinitesimal
1.4.2 Infinite
Exercise1.4
1.5 Continuou.s Function
1.5.1 Continuity
1.5.2 Discontinuity
Exercise1.5
1.6 Theorems about Continuous Function on a Closed Interval
Exercise 1.6
Review and Exercise
Chapter 2 Differentiation
2.1 The Derivative
Exercise 2.1
2.2 Rules for Fingding the Derivative
2.2.1 Derivative of Arithmetic Combination
2.2.2 The Derivative Rule for Inverses
2.2.3 Derivative of Composition
2.2.4 Implicit Differentiation
2.2.5 Parametric Differentiation
2.2.6 Related Rates of Change
Exercise 2.2
2.3 Higher—Order Derivatives
Exercise 2.3
2.4 Differentials
Exercise 2.4
2.5 The Mean Value Theorem
Exercise 2.5
2.6 LHopitals Rule
Exercise 2.6
2.7 Taylors Theorem
Exercise 2.7
2.8 Applications of Derivatives
2.8.1 Monotonicity
2.8.2 Local Extreme Values
2.8.3 Extreme Values
2.8.4 Concavity
2.8.5 Graphing Functions
Exercise 2.8
Review and Exercise
Chapter3 The Integration
3.1 The Definite Integral
3.1.1 Two Examples
3.1.2 The Definition of Definite Integral
3.1.3.Properties of Definite Integrals
Exercise 3.1
3.2 The Indefinite Integral
Exercise 3.2
3.3 The Fundamental Theorem
3.3.1 First Fundamental Theorem
3.3.2 Second Fundamental Theorem
Exercise 3.3
3.4 Techniques of Indefinite Integration
3.4.1 Substitution in Indefinite Integrals
3.4.2 Indefinite Integration by Parts
3.4.3 Indefinite Integration of Rational Functions by Partial Fractions
Exercise 3.4
3.5 Techniques of Definite Integration
3.5.1 Substitution in Definite Integrais
3.5.2 Definite Integration by Parts
Exercise 3.5
3.6 AppLications of Definite Integrals
3.6.1 Lengths of Plane Curves
3.6.2 Area between Two Curves
3.6.3 Volumes of Solids
3.6.4 Areas of Surface of Revolution
3.6.5 Moments and Center of Mass
3.6.6 Work and Fluid Force
Exercise 3.6
3.7 Improper Integrals
3.7.1 Improper Integrals： Infinite I.imits of Integration
3.7.2 Improper Integrals： Infinite Integrands
Exercise 3.7
Review and Exercise
Chapter 4 Differential Equations
4.1 The Concept of Differential Equations
Exercise 4.1
4.2 Differential Equations of the First Order
4.2.1 Equations with Variable Separable
4.2.2 Homogeneous Equation
Exercise 4.2
4.3 First—order Linear Differential Equations
Exercise 4.3
4.4 Equations Reducible to First Order
4.4.1 Equations of the Form y（n） = f （ x）
4.4.2 Equations of the Form y"= f （x，y）
4.4.3 Equations of the Form y"= f（y，y）
Exercise 4.4
4.5 Linear Differential Equations
4.5.1 Basic Theory of Linear Differential Equations
4.5.2 Homogeneous Linear Differential Equations of the Second Order with Constant Coefficients
4.5.3 Nonhomogeneous I.inear Differential Equations of the Second Order with Constant Coefficients
4.5.4 Euler Differential Equation
Exercise 4.5
4.6 Systems of Linear Differential Equations with Constant Coefficients
Exercise 4.6
4.7 Applications
Exercise 4.7
Review and Exercise
内容摘要
《高等院校双语教学规划教材:高等数学(上册)(英文版)》是为响应东南大学靠前化需要，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。全书分为上、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、向量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。
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