高等数学（I,II）（英文版）
￥99.00定价
作者： 侯书会
出版时间：2023-04
出版社：科学出版社
- 科学出版社
- 9787030480453
- 1-1
- 53307
- 0044178751-2
- 平装
- 2023-04
- 760
- 458
- 理学
- 数学
- O13
- 双语教学
- 公共课
内容简介
侯书会、刘白羽编的《高等数学(共2册)(英文版)》分上、下两册出版。上册共七章，着重介绍一元微积分学的基础理论知识。内容包括函数、极限、函数连续性，导数、微分及其应用，不定积分、定积分及其应用；下册共六章，着重介绍多元微分学的基础理论知识。内容包括无穷级数、向量代数与空间解析几何，多元函数、极限及其连续性，多元函数的微分及应用，重积分、曲线积分、曲面积分及常微分方程。
本书是基于多年教学经验，兼顾国内工科类本科数学基础要求和海外学习的双重需要编写而成的。与经典的中文微积分教材相比，本书适当降低了难度，突出了微积分学和后续应用型课程中常用的计算和证明方法。在保证教材内容符合学科要求且不低于本科阶段微积分课程教学标准的前提下，力求语言精准、简练，以适应我国学生的外语水平和学习特点。
本书适于作为工科院校的国际班、双语教学班的高等数学教材和参考书。
本书是基于多年教学经验，兼顾国内工科类本科数学基础要求和海外学习的双重需要编写而成的。与经典的中文微积分教材相比，本书适当降低了难度，突出了微积分学和后续应用型课程中常用的计算和证明方法。在保证教材内容符合学科要求且不低于本科阶段微积分课程教学标准的前提下，力求语言精准、简练，以适应我国学生的外语水平和学习特点。
本书适于作为工科院校的国际班、双语教学班的高等数学教材和参考书。
目录
Chapter 1 Preliminaries
1.1 Some Set Theory Notation for the Study of Calculus
1.1.1 Definition of Set
1.1.2 Descriptions of set
1.1.3 Set Operations
1.1.4 Interval
1.1.5 Neighbourhood
1.2 The Rectangular Coordinate System
1.2.1 Cartesian Coordinates
1.2.2 Distance Formula
1.2.3 The Equation of a Circle
1.3 The Straight Line
1.3.1 The Slope of a Line
1.3.2 The Equation of a Line
1.4 Graphs of Equations
1.4.1 The Graphing Procedure
1.4.2 Symmetry of a Graph
1.4.3 Intercepts
1.4.4 Problems for Chapter 1
Chapter 2 Functions and Limits
2.1 Functions
2.1.1 Definition of Function
2.1.2 Properties of Functions
2.1.3 Operations on Functions
2.1.4 Elementary Functions
2.1.5 Problems for Section 2.1
2.2 Limits
2.2.1 Introduction to Limits
2.2.2 Definition of Limit
2.2.3 Operations on Limits
2.2.4 Limits at Infinity and Infinite Limits
2.2.5 Infinitely Small Quantity (or Infinitesimal)
2.2.6 Problems for Section 2.2
2.3 Continuity of Functions
2.3.1 Definition of Continuity
2.3.2 Continuity under Function Operations
2.3.3 Continuity of Elementary Functions
2.3.4 Intermediate Value Theorem
2.3.5 Problems for Section 2.3
2.4 Chapter Review
2.4.1 Drills
2.4.2 Sample Test Problems
Chapter 3 Differentiation
3.1 Derivatives
3.1.1 Two Problems with One Theme
3.1.2 Definition
3.1.3 Rules for Finding Derivatives
3.1.4 Problems for Section 3.1
3.2 Higher-Order Derivatives
3.2.1 Definition
3.2.2 Sum, Difference and Product Rules
3.2.3 Problems for Section 3.2
3.3 Implicit Differentiation
3.3.1 Guidelines for implicit Differentiation
3.3.2 Related Rates
3.3.3 Problems for Section 3.3
3.4 Differentials and Approximations
3.4.1 Definition of Differential
3.4.2 Differential Rules
……
Chapter 4 Applications of Differentiation
Chapter 5 Indefinite Integrals
Chapter 6 Definite Integrals
Chapter 7 Applications of Integration
Chapter 8 Infinite Series
Chapter 9 Geometry in Space and Vectors
Chapter 10 Derivatives for Functions of Two or More Variables
Chapter 11 Multiple Integrals
Chapter 12 Vector Calculus
Chapter 13 Differential Equations
References
1.1 Some Set Theory Notation for the Study of Calculus
1.1.1 Definition of Set
1.1.2 Descriptions of set
1.1.3 Set Operations
1.1.4 Interval
1.1.5 Neighbourhood
1.2 The Rectangular Coordinate System
1.2.1 Cartesian Coordinates
1.2.2 Distance Formula
1.2.3 The Equation of a Circle
1.3 The Straight Line
1.3.1 The Slope of a Line
1.3.2 The Equation of a Line
1.4 Graphs of Equations
1.4.1 The Graphing Procedure
1.4.2 Symmetry of a Graph
1.4.3 Intercepts
1.4.4 Problems for Chapter 1
Chapter 2 Functions and Limits
2.1 Functions
2.1.1 Definition of Function
2.1.2 Properties of Functions
2.1.3 Operations on Functions
2.1.4 Elementary Functions
2.1.5 Problems for Section 2.1
2.2 Limits
2.2.1 Introduction to Limits
2.2.2 Definition of Limit
2.2.3 Operations on Limits
2.2.4 Limits at Infinity and Infinite Limits
2.2.5 Infinitely Small Quantity (or Infinitesimal)
2.2.6 Problems for Section 2.2
2.3 Continuity of Functions
2.3.1 Definition of Continuity
2.3.2 Continuity under Function Operations
2.3.3 Continuity of Elementary Functions
2.3.4 Intermediate Value Theorem
2.3.5 Problems for Section 2.3
2.4 Chapter Review
2.4.1 Drills
2.4.2 Sample Test Problems
Chapter 3 Differentiation
3.1 Derivatives
3.1.1 Two Problems with One Theme
3.1.2 Definition
3.1.3 Rules for Finding Derivatives
3.1.4 Problems for Section 3.1
3.2 Higher-Order Derivatives
3.2.1 Definition
3.2.2 Sum, Difference and Product Rules
3.2.3 Problems for Section 3.2
3.3 Implicit Differentiation
3.3.1 Guidelines for implicit Differentiation
3.3.2 Related Rates
3.3.3 Problems for Section 3.3
3.4 Differentials and Approximations
3.4.1 Definition of Differential
3.4.2 Differential Rules
……
Chapter 4 Applications of Differentiation
Chapter 5 Indefinite Integrals
Chapter 6 Definite Integrals
Chapter 7 Applications of Integration
Chapter 8 Infinite Series
Chapter 9 Geometry in Space and Vectors
Chapter 10 Derivatives for Functions of Two or More Variables
Chapter 11 Multiple Integrals
Chapter 12 Vector Calculus
Chapter 13 Differential Equations
References
