- 高等数学(上英文版第2版21世纪高等学校双语教材)
- - 作者：编者:陈文彦//马红铝|责编:吉雄飞
  - 出版社：东南大学
  - ISBN：9787576613896
  - 出版日期：2024/05/01
  - 页数：298
- 售价：20.72

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本书是为响应东南大学国际化需求，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，此为上册，主要内容包括极限和连续、一元函数微分学、一元函数积分学、常微分方程等。本书按国内高等数学教材体系进行编排，相比国外教材要简洁，同时兼顾美国教材重视应用、便于自学的特点。本书可作为高等院校工科类专业本科生学习高等数学的英文教材，也可供其他专业学生选用和相关科技工作者参考。
作者介绍
目录
Chapter 1  Limit and Continuity
  1.1  Functions
    1.1.1  Mopping
    1.1.2  Function of Single Vorioble
    1.1.3  Elementory Functions ond Hyperbolic Functions
    Exercise 1.1
  1.2  The Concept of Limits and its Properties
    1.2.1  Limits of Sequence
    1.2.2  Limits of Functions
    1.2.3  Properties of Limits
    Exercise 1.2
  1.3  Rules for Finding Limits
    1.3.1  Operation on Limits
    1.3.2  Limits Theorem
    1.3.3  Two Important Special Limits
    Exercise 1.3
  1.4  Infinitesimal and Infinite
    1.4.1  Infinitesimal
    1.4.2  Infinite
    1.4.3  Comparison between Infinitesimal
    Exercise 1.4
  1.5  Continuous Function
    1.5.1  Continuity
    1.5.2  Continuity of Elementary Functions
    1.5.3  Discontinuity
    1.5.4  Theorems about Continuous Functions on a Closed Interval
    Exercise 1.5
  Chapter Review Exercise
Chapter 2  Differentiation
  2.1  The Derivative
    2.1.1  Two Problems with one Theme
    2.1.2  Definition of the Derivative
    2.1.3  Geometric Interpretation of the Derivative
    2.1.4  The Relationship between Differentiability and Continuity
    Exercise 2.1
  2.2  Finding Rules for Derivative
    2.2.1  Derivative of Basic Elementary Functions
    2.2.2  Derivative of Arithmetic Combination
    2.2.3  The Derivative Rule for Inverses
    2.2.4  Derivative of Composition
    2.2.5  Implicit Differentiation
    2.2.6  Parametric Differentiation
    2.2.7  Related Rates of Change
    Exercise 2.2
  2.3  Higher-Order Derivatives
    Exercise 2.3
  2.4  Differentials
    2.4.1  Definition of Differentials
    2.4.2  Differential Rules
    2.4.3  Application of Differentials in Approximation

    Exercise 2.4
  2.5  The Mean Value Theorem
    2.5.1  Fermat's Theorem
    2.5.2  Rolle's Theorem
    2.5.3  Lagrange's Theorem
    2.5.4  Cauchy's Theorem
    Exercise 2.5
  2.6  L'Hopital's Rule
    2.6.1  Indeterminate Forms of Type 0/0
    2.6.2  Indeterminate Forms of Type ∞/∞
    2.6.3  Other Indeterminate Forms
    Exercise 2.6
  2.7  Taylor's Theorem
    Exercise 2.7
  2.8  Applications of Derivatives
    2.8.1  Monotonicity
    2.8.2  Local Extreme Values
    2.8.3  Global Maxima and Minima
    2.8.4  Concavity
    2.8.5 Asymptote
    2.8.6  Graphing Functions
    Exercise 2.8
  Chapter Review Exercise
Chapter 3  Integration
  3.1  The Definite Integral
    3.1.1  Two Examples
    3.1.2  Properties of Definite Integral
    Exercise 3.1
  3.2  The Fundamental Theorem
    3.2.1  Newton-Leibniz Formula
    3.2.2  The First Fundamental Theorem of Calculus
    Exercise 3.2
  3.3  The Indefinite Integral
    3.3.1  The Definition of Indefinite Integral
    3.3.2  Substitution in Indefinite Integrals
    3.3.3  Indefinite Integration by Parts
    3.3.4  Indefinite Integration of Rational Functions by Partial Fractions
    Exercise 3.3
  3.4  Techniques of Definite Integration
    3.4.1  Substitution in Definite Integrals
    3.4.2  Definite Integration by Parts
    Exercise 3.4
  3.5  Applications of Definite Integrals
    3.5.1  Infinite Sum Theorem
    3.5.2  Area between Two Curves
    3.5.3  Volumes of Solids
    3.5.4  Lengths of Plane Curves
    3.5.5  Areas of Surface of Revolution
    3.5.6  Mass and Center of Mass
    3.5.7  Work and Fluid Force

    Exercise 3.5
  3.6  Improper Integrals
    3.6.1  The proposition of Improper Integrals
    3.6.2  Improper Integrals..Infinite Limits of Integration
    3.6.3  Improper Integrals: Infinite Integrands
    Exercise 3.6
  3.7  Tests for Improper Integrals
    3.7.1  Test for Improper Integrals: Infinite Limits of Integration
    3.7.2  Test for Improper Integrals.Infinite Integrands
    3.7.3  The Gamma Function
    Exercise 3.7
  Chapter Review Exercise
Chapter 4  Differential Equations
  4.1  Differential Equations of the First Order
    4.1.1  The Concept of Differential Equations
    4.1.2  Equations with Variable Separable
    4.1.3  Homogeneous Equation
    4.1.4  First-Order Linear Differential Equations
    4.1.5  Equations Reducible to First-Order
    Exercise 4.1
  4.2  Linear Differential Equations
    4.2.1  Basic Theory of Linear Differential Equations
    4.2.2  Linear Differential Equations of the Second-Order with Constant Coefficients
    4.2.3  Euler Differential Equation
    Exercise 4.2
  4.3  Systems of Linear Differential Equations with Constant Coefficients
    Exercise 4.3
  4.4  Applications of Ordinary Derivative Equation
    Exercise 4.4
  Chapter Review Exercise
Solutions to Selected Problem

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