高等数学（英文版）（Ⅰ、Ⅱ）
作者： 侯书会
出版时间：2016年5月
出版社：中国科技出版传媒股份有限公司
- 中国科技出版传媒股份有限公司
- 9787030480453
- 1-1
- 53307
- 0044178751-2
- 平装
- 大大32开
- 2016年5月
- 760
- 458
- 理学
- 数学
- O13
- 双语教学
- 本科
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。
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
