本书分上、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。

Contents
Chapter lPreliruinaries
I.I 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
Chapter 2Functions and Limits
2.1 Functions
2.1.1 Definition of Function
2.1.2 Properties of Functions
2.1.3 0perations on Functions
2.1.4 Elementary Functions
2.1.5 Problems for Section 2.
2.2 Limits
2.2.1 Introduction to Limits
2.2.2 Definition of Limit
2.2.3 0perations 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.
2.3 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.
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.
3.2 Higher-Order Derivatives
3.2.1 Definition
3.2.2 Sum, Difference and Product Rules
3.2.3 Problems for Section 3.
3.3 Implicit Differentiation
3.3.1 Guidelines for implicit Differentiation
3.3.2 Related Rates
3.3.3 Problems for Section 3.
3.4 Differentials and Approximations
3.4.1 Definition of Differential
3.4.2 Differential Rules
3.4.3 Approximations
3.4.4 Problems for Section 3.
3.5 Chapter Review
3.5.1 Drills
3.5.2 Sample Test Problems
Chapter 4 Applications of Differentiation
4.1 Maxima and Minima
4.1.1 Extrema on an Interval
4.1.2 Problems for Section 4.
4.2 Monotonicity and Concavity
4.2.1 The First Derivative and Monotonicity
4.2.2 The Second Derivative and Concavity
4.2.3 Problems for Section 4.
4.3 Local Maxima and Minima
4.3.1 Definition
4.3.2 Tests for Local Maxima and Minima
4.3.3 More Maxima and Minima Problems
4.3.4 Problems for Section 4.
4.4 Sophisticated Graphing
4.4.1 Asymptote
4.4.2 Sophisticated Graphing
4.4.3 Problems for Section 4.
4.5 The Mean Value Theorem
4.5.1 Rolle's Theorem
4.5.2 Lagrange's Mean Value Theorem
4.5.3 Cauchy's Mean Value Theorem
4.5.4 Problems for Section 4.
4.6 L'Hopital's Rule
4.6.1 Indeterminate Forms of Type
4.6.2 Indeterminate Forms of Type里
4.6.3 0ther Indeterminate Forms
4.6.4 Problems for Section 4.
4.7 Chapter Review
4.7.1 Drills
4.7.2 Sample Test Problems
Chapter5 Indefinite Integrals
5.1 Definition and Properties of Indefinite Integrals
5.1.1 Definition of Indefinite Integrals
5.1.2 Standard Integral Forms
5.1.3 Properties of' Indefinite Integrals
5.1.4 Problems for Section 5.
5.2 Integration by Substitution
5.2.1 The Mehod of Substitution
5.2.2 Rationalizing Substitutions
5.2.3 0ther Substitutions (Inverse)
5.2.4 Problems for Section 5.
5.3 Integration by Parts
5.3.1 Problems for Section 5.
5.4 Integration of Rational Functions
5.4.1 Partial Fraction Decompositions
5.4.2 Integration of Rational Functions Using Partial Fractions
5.4.3 Problems for Section 5.
5.5 Chapter Review
5.5.1 Drills
5.5.2 Sample Test Problems
Chapter6 Definite Integrals
6.1 D