本书是“世界优秀教材中国版”系列教材之一,从Wiley出版公司引进，由国内专家改编。本书强调对概念的理解，包括描述性的直观理解，数值和图像的处理等，以达到严格的数学定义。另外，本书在许多章最后部分给出实际数学模型，有助于提高学生的学习兴趣。改编者根据我国微积分教学计划，删除一些中国学生中学已经学过的内容，如反三角函数、指数函数、对数函数等；对微积分课程中涉及不多的内容进行了简化，如图形计算部分；对附录内容也进行了适当改动。这样使本书更符合我国教学大纲要求，适合中国学生使用。 本书适合高等院校理工科各专业本科学生作为微积分双语教材使用，也适用于自学者。
- 前辅文
- chapter one FUNCTIONS
- 1.1 Functions
- 1.2 Arithmetic Operations on and Composition of Functions
- 1.3 Families of Functions
- 1.4 Inverse Functions
- 1.5 Exponential and Logarithmic Functions
- 1.6 Parametric Equations
- chapter two LIMITS AND CONTINUITY
- 2.1 Limits(An Intuitive Approach)
- 2.2 Computing Limits
- 2.3 Limits at Infinity
- 2.4 Limits (Discussed More Rigorously)
- 2.5 Continuity
- 2.6 Continuity of Trigonometric and Inverse Functions
- chapter three THE DERIVATIVE
- 3.1 Tangent Lines, Velocity, and General Rates of Change
- 3.2 The Derivative Function
- 3.3 Techniques of Differentiation
- 3.4 The Product and Quotient Rules
- 3.5 Derivatives of Trigonometric Functions
- 3.6 The Chain Rule
- 3.7 Related Rates
- 3.8 Local Linear Approximation
- chapter four DERIVATIVES OF LOGARITHMIC, EXPONENTIAL, AND INVERSE TRIGONOMETRIC FUNCTIONS
- 4.1 Implicit Differentiation
- 4.2 Derivatives of Logarithmic Functions
- 4.3 Derivatives of Exponential and Inverse Trigonometric Functions
- 4.4 L’H pital’s Rule
- chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS
- 5.1 Analysis of Functions I: Increase, Decrease, and Concavity
- 5.2 Analysis of Functions II: Relative Extrema
- 5.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines
- 5.4 Absolute Maxima and Minima
- 5.5 Applied Maximum and Minimum Problems
- 5.6 Rolle’s Theorem
- chapter six INTEGRATION
- 6.1 An Overview of the Area Problem
- 6.2 The Indefinite Integral
- 6.3 Integration by Substitution
- 6.4 The Definition of Area as a Limit
- 6.5 The Definite Integral
- 6.6 The Fundamental Theorem of Calculus
- 6.7 Evaluating Definite Integrals by Substitution
- 6.8 Logarithmic Functions from the Integral Point of View
- chapter seven APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY AND ENGINEERING
- 7.1 Area Between Two Curves
- 7.2 Volumes by Slicing
- 7.3 Volumes by Cylindrical Shells
- 7.4 Length of a Plane Curve
- 7.5 Work
- 7.6 Fluid Pressure and Force
- chapter eight PRINCIPLES OF INTEGRAL EVALUATION
- 8.1 Integration by Parts
- 8.2 Trigonometric Integrals
- 8.3 Trigonometric Substitutions
- 8.4 Integrating Rational Functions by Partial Fractions
- 8.5 Improper Integrals
- chapter nine MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
- 9.1 First-Order Differential Equations and Applications
- 9.2 Modeling with First-Order Differential Equations
- 9.3 Second-Order Linear Homogeneous Differential Equations
- chapter ten INFINITE SERIES
- 10.1 Sequences
- 10.2 Monotone Sequences
- 10.3 Infinite Series
- 10.4 Convergence Tests
- 10.5 The Comparison, Ratio, and Root Tests
- 10.6 Alternating Series
- 10.7 Maclaurin and Taylor Polynomials
- 10.8 Maclaurin and Taylor Series
- 10.9 Convergence of Taylor Series
- 10.10 Differentiating and Integrating Power Series
- chapter eleven THREE-DIMENSIONAL SPACE
- 11.1 Rectangular Coordinates in 3-Space; Spheres
- 11.2 Vectors
- 11.3 Dot Product
- 11.4 Cross Product
- 11.5 Parametric Equations of Lines
- 11.6 Planes in 3-Space
- 11.7 Quadric Surfaces
- 11.8 Cylindrical and Spherical Coordinates
- chapter twelve VECTOR-VALUED FUNCTIONS
- 12.1 Introduction to Vector-Valued Functions
- 12.2 Calculus of Vector-Valued Functions
- chapter thirteen PARTIAL DERIVATIVES
- 13.1 Functions of Two or More Variables
- 13.2 Limits and Continuity
- 13.3 Partial Derivatives
- 13.4 Differentiability, Differentials, and Local Linearity
- 13.5 The Chain Rule
- 13.6 Directional Derivatives and Gradients
- 13.7 Tangent Planes and Normal Vectors
- 13.8 Maxima and Minima of Functions of Two Variables
- 13.9 Lagrange Multipliers
- chapter fourteen MULTIPLE INTEGRALS
- 14.1 Double Integrals
- 14.2 Double Integrals over Nonrectangular Regions
- 14.3 Double Integrals in Polar Coordinates
- 14.4 Parametric Surfaces
- 14.5 Triple Integrals
- 14.6 Triple Integrals in Cylindrical and Spherical Coordinates
- 14.7 Change of Variables in Double Integrals
- chapter fifteen TOPICS IN VECTOR CALCULUS
- 15.1 Vector Fields
- 15.2 Line Integrals
- 15.3 Independence of Path
- 15.4 Green’s Theorem
- 15.5 Surface Integrals
- 15.6 Applications of Surface Integrals
- 15.7 The Divergence Theorem
- 15.8 Stokes’ Theorem
- appendix
- SELECTED PROOFS
- ANSWERS TO SELECTED EXERCISES
- GLOSSARY
