本书是英文版大学数学微积分教材，分为上、下两册。上册为单变量微积分学，包括函数、极限和连续、导数、中值定理及导数的应用以及一元函数积分学等内容；下册为多变量微积分学，包括空间解析几何及向量代数、多元函数微分学、重积分、线积分与面积分、级数及微分方程初步等内容。
本书由两位国内作者和一位外籍教授共同完成，在内容体系安排上与国内主要微积分教材一致，同时也充分参考和借鉴了国外尤其是北美一些大学微积分教材的诸多特点，内容深入浅出，语言简洁通俗。
本书适合作为大学本科生一学年微积分教学的教材，也可作为非英语教学的参考书。
- CHAPTER 5 Vectors and the Geometry of Space
- 5.1 Vectors
- 5.1.1 Concepts of Vectors
- 5.1.2 Linear Operations Involving Vectors
- 5.1.3 Coordinate Systems in Three Dimensional Space
- 5.1.4 Representing Vectors Using Coordinates
- 5.1.5 Lengths,Direction Angles and Projections of Vectors
- 5.2 Dot Product,Cross Product and Scalar Triple Product
- 5.2.1 The Dot Product
- 5.2.2 The Cross Product
- 5.2.3 Scalar Triple Product
- 5.3 Equations of Planes and Lines
- 5.4 Surfaces In Space
- 5.4.1 Surfaces and Equations
- 5.4.2 Cylinder
- 5.4.3 Surface of Revolution
- 5.4.4 Quadric Surfaces
- 5.5 Curves in Space
- 5.5.1 General Equations of Curves in the Space
- 5.5.2 Parametric Equations of Curves in the Space
- 5.5.3 Parametric Equations of Surfaces in the Space
- 5.5.4 Projections of Curves in the Space
- 5.6 Exercises
- 5.6.1 Vectors
- 5.6.2 Planes and Lines in Space
- 5.6.3 Surfaces and Curves in Space
- 5.6.4 Questions to Guide Your Revision
- CHAPTER 6 Functions of Several Variables
- 6.1 Functions of Several Variables
- 6.1.1 Definition
- 6.1.2 Limits
- 6.1.3 Continuity
- 6.2 Partial Derivatives
- 6.2.1 Definition
- 6.2.2 Partial Derivative of Higher Order
- 6.3 Total Differential
- 6.3.1 Definition
- 6.3.2 The Total Differential Approximation
- 6.4 The Chain Rule
- 6.5 Implicit Differentiation
- 6.5.1 Functions Defined by a Single Equation
- 6.5.2 Functions Defined Implicitly by System of Equations
- 6.6 Applications of the Differential Calculus
- 6.6.1 Tangent Lines and Normal Planes
- 6.6.2 Tangent Planes and Normal Lines for Surfaces
- 6.7 Directional Derivatives and Gradient Vectors
- 6.8 Maximum and Minimum
- 6.8.1 Extrema of Functions of Several Variables
- 6.8.2 Lagrange Multipliers
- 6.9 Additional Materials
- 6.9.1 Taylors Theorem for Functions of Two Variables
- 6.9.2 Clairaut
- 6.9.3 Cobb Douglas Production Function
- 6.10 Exercises
- 6.10.1 Functions of Several Variables
- 6.10.2 Applications of Partial Derivatives
- 6.10.3 Questions to Guide Your Revision
- CHAPTER 7 Multiple Integrals
- 7.1 Definition and Properties
- 7.2 Iterated Integrals
- 7.2.1 Iterated Integrals in Rectangular Coordinates
- 7.2.2 Change of Variables Formula for Double Integrals
- 7.3 Triple Integrals
- 7.3.1 Triple Integrals in Rectangular Coordinates
- 7.3.2 Change of Variables in Triple Integrals
- 7.4 The Area of a Surface
- 7.5 Additional Materials
- 7.6 Exercises
- 7.6.1 Double Integrals
- 7.6.2 Triple Integrals
- 7.6.3 Applications of Multiple Integrals
- 7.6.4 Questions to Guide Your Revision
- CHAPTER 8 Line and Surface Integrals
- 8.1 Line Integrals
- 8.1.1 Introduction
- 8.1.2 Definition of the Line Integral with Respect to Arc Length
- 8.1.3 Evaluating Line Integrals,∫Cf(x, y)ds,in R2
- 8.1.4 Evaluating Line Integrals,∫Cf(x,y,z)ds,in R3
- 8.2 Vector Fields，Work，and Flows
- 8.2.1 Introduction
- 8.2.2 The Line Integral of a Vector Field Along a Curve C
- 8.2.3 Different Forms of the Line Integral Including ∫CF→·dr→
- 8.2.4 Examples of Line Integrals
- 8.3 Greens Theorem in R2
- 8.3.1 The Circulation Curl Form of Greens Theorem
- 8.3.2 The Divergence Flux Form of Greens Theorem
- 8.3.3 Generalized Greens Theorem
- 8.4 Path Independent Line Integrals and Conservative Fields
- 8.4.1 Introduction
- 8.4.2 Fundamental Results on Path Independent Line Integrals
- 8.5 Surface Integrals
- 8.5.1 Definition of Integration With Respect to Surface Area
- 8.5.2 Evaluation of Surface Integrals
- 8.6 Surface Integrals of Vector Fields
- 8.6.1 Definition and Properties of Flux,SF→·N→dS
- 8.6.2 Evaluating SF→·N→dS for a Surface z=z(x,y)
- 8.7 The Divergence Theorem
- 8.7.1 Introduction
- 8.7.2 Physical interpretation of the Divergence SymbolQC@·F→(x,y,z)
- 8.8 Stokes Theorem
- 8.9 Additional Materials
- 8.9.1 Green
- 8.9.2 Gauss
- 8.9.3 Stokes
- 8.10 Exercises
- 8.10.1 Line Integrals
- 8.10.2 Surface Integrals
- 8.10.3 Questions to Guide Your Revision
- CHAPTER 9 Infinite Sequences,Series and Approximations
- 9.1 Infinite Sequences
- 9.2 Infinite Series
- 9.2.1 Definition of Infinite Series
- 9.2.2 Properties of Convergent Series
- 9.3 Tests for Convergence
- 9.3.1 Series with Nonnegative Terms
- 9.3.2 Series with Negative and Positive Terms
- 9.4 Power Series and Taylor Series
- 9.4.1 Power Series
- 9.4.2 Working with Power Series
- 9.4.3 Taylor Series
- 9.4.4 Applications of Power Series
- 9.5 Fourier Series
- 9.5.1 Fourier Series Expansion with Period 2π
- 9.5.2 Fourier Cosine and Sine Series with Period 2π
- 9.5.3 The Fourier Series Expansion with Period 2l
- 9.5.4 Fourier Series with Complex Terms
- 9.6 Additional Materials
- 9.6.1 Fourier
- 9.6.2 Maclaurin
- 9.6.3 Taylor
- 9.7 Exercises
- 9.7.1 Series with Constant Terms
- 9.7.2 Power Series
- 9.7.3 Fourier Series
- 9.7.4 Questions to Guide Your Revision
- CHAPTER 10 Introduction to Ordinary Differential Equation
- 10.1 Differential Equations and Mathematical Models
- 10.2 Methods for Solving Ordinary Differential Equations
- 10.2.1 Separable Equations
- 10.2.2 Substitution Methods
- 10.2.3 Exact Differential Equations
- 10.2.4 Linear First Order Differential Equations and Integrating Factors
- 10.2.5 Reducible Second Order Equations
- 10.2.6 Linear Second Order Differential Equations
- 10.3 Other Ways of Solving Differential Equations
- 10.3.1 Power Series Method
- 10.3.2 Direction Fields
- 10.3.3 Numerical Approximation:Eulers Method
- 10.4 Additional Materials
- 10.4.1 Euler
- 10.4.2 Bernoulli
- 10.4.3 The Bernoulli Family
- 10.4.4 Development of Calculus
- 10.5 Exercises
- 10.5.1 Introduction to Differential Equations
- 10.5.2 First Order Differential Equation
- 10.5.3 Second Order Differential Equation
- 10.5.4 Questions to Guide Your Revision
- Answers
- Reterence Books
