这是一本在美国大学中使用面比较广泛的微积分教材。有重视应用、便于自学、习题数量与内容比较丰富等特点。而与其他美国教材的差别在于严谨性，本书许多定理都有较严谨的证明，这一点与我国许多现行的理工科微积分教材比较类似。在美国也是另一种风格的教材。

本书强调应用，习题数量多，类型多，重视不同数学学科之间的交叉，强调其实际背景，反映当代科技发展。每章之后有附加内容，有利用图形计算器或数学软件计算的习题或带研究性的小题目等。

出版说明

序

Preface

0 Preliminaries

 0.1 Real Numbers.Estimation，and Logic

 0.2 Inequalities and Absolute Values

 0.3 The Rectangular Coordinate System

 0.4 Graphs of Equations

 0.5 Functions and Their Graphs

 0.6 Operations on Functions

 0.7 Trigonometric Functions

 0.8 Chapter Review

 Review and Preview Problems

1 Limits

 1.1 Introduction to Limits

 1.2 Rigorous Study of Limits

 1.3 Limit Theorems

 1.4 Limits Involving Trigonometric Functions

 1.5 Limits at Infinity；Infinite Limits

 1.6Continuity of Functions

 1.7Chapter Review

 Review and Preview Problems

2 The Derivative

 2.1 Two Problems with One Theme

 2.2 The Derivative

 2.3 Rules for Finding Derivatives

 2.4 Derivatives of Trigonometric Functions

 2.5 The Chain Rule

 2.6 Higher.Order Derivatives

 2.7 Implicit Differentiation

 2.8 Related Rates

 2.9 Differentials and Approximations

 2.10 Chapter Review

 Review and Preview Problems

3 Applications of the Derivative

 3.1 Maxima and Minima

 3.2 Monotonicity and Concavity

 3.3 Local Extrema and Extrema on Open Intervals

 3.4 Practical Problems

 3.5 Graphing Functions Using Calculus

 3.6 The Mean Value Theorem for Derivatives

 3.7 Solving Equations Numerically

 3.8 Antiderivatives

 3.9 Introduction to Differential Equations

 3.10 Chapter Review

 Review and Preview Problems

4 The Deftnite Integral

 4.1 Introduction to Area

 4.2 The Definite Integral

 4.3 The First Fundamental Theorem of Calculus

 4.4 The Second Fundamental Theorem of Calculus and the Method of Substitution

 4.5 The Mean Value Theorem for Integrals and the Use of Symmetry

 4.6 Numerical Integration

 4.7 Chapter Review

 Review and Preview Problems

5 Applications of the Integral

 5.1 The Area of a Plane Region

 5.2 volumes of Solids：Slabs.Disks,Wlashers

 5.3 Volumes of Solids of Revolution：Shells

 5.4 Length of a Plane Curve

 5.5 Work and Fluid Force

 5.6 Moments and Center of Mass

 5.7 Probability and Random Variabtes

 5.8 Chapter Review322

 Review and Preview Problems

6 Transcendental Functions

 6.1 The Natural Logarithm Function

 6.2 Inverse Functions and Their Derivatives

 6.3 The Natural Exponential Function

 6.4 General Exponential and Logarithmic Functions

 6.5 Exponential Growth and Decay

 6.6 First.Order Linear Differential Equations

 6.7 Approximations for Differential Equations

 6.8 The Inverse Trigonometric Functions and Their Derivatives

 6.9 The Hyperbolic Functions and Their Inverses

 6.10 Chapter Review

 Review and Preview Problems

7 Techniques of Integration

 7.1 Basic Integration Rules

 7.2 Integration by Parts

 7.3 Some Trigonometric Integrals

 7.4 Rationalizing Substitutions

 7.5 Integration of Rational Functions Using Partial Fractions

 7.6 Strategies for Integration

 7.7 Chapter Review

 Review and Preview Problems

8 Indeterminate Forms and Improper

 Integrals

 8.1 Indeterminate Forms of Type 0/0

 8.2 Other Indeterminate Forms

 8.3 Improper Integrals: Infinite Limits of Integration

 8.4 Improper Integrals: Infinite Integrands

 8.5 Chapter Review

 Review and Preview Problems

9 Infinite Series

 9.1 Infinite Sequences

 9.2 Infinite Series

 9.3 Positive Series: The Integral Test

 9.4 Positive Series: Other Tests

 9.5 Alternating Series, Absolute Convergence, and Conditional Convergence

 9.6 Power Series

 9.7 Operations on Power Series

 9.8 Taylor and Maclaurin Series

 9.9 The Taylor Approximation to a Function

 9.10 Chapter Review

 Review and Preview Problems

10 Conics and Polar Coordinates

 10.1 The Parabola

 10.2 Ellipses and Hyperbolas

 10.3 Translation and Rotation of Axes

 10.4 Parametric Representation of Curves in the Plane

 10.5 The Polar Coordinate System

 10.6 Graphs of Polar Equations

 10.7 Calculus in Polar Coordinates

 10.8 Chapter Review

 Review and Preview Problems

11 Geometry in Space and Vectors

 11.1 Cartesian Coordinates in Three-Space

 11.2 Vectors

 11.3 The Dot Product

 11.4 The Cross Product

 11.5 Vector-Valued Functions and Curvilinear Motion

 11.6 Lines and Tangent Lines in Three-Space

 11.7 Curvature and Components of Acceleration

 11.8 Surfaces in Three-Space

 11.9 Cylindrical and Spherical Coordinates

 11.10 Chapter Review

 Review and Preview Problems

12 Derivatives for Functions of Two or More Variables

 12.1 Functions of Two or More Variables

 12.2 Partial Derivatives

 12.3 Limits and Continuity

 12.4 Differentiability

 12.5 Directional Derivatives and Gradients

 12.6 The Chain Rule

 12.7 Tangent Planes and Approximations

 12.8 Maxima and Minima

 12.9 The Method of Lagrange Multipliers

 12.10 Chapter Review

 Review and Preview Problems

13 Multiple Integrals

 13.1 Double Integrals over Rectangles

 13.2 Iterated Integrals

 13.3 Double Integrals over Nonrectangular Regions

 13.4 Double Integrals in Polar Coordinates

 13.5 Applications of Double Integrals

 13.6 Surface Area

 13.7 Triple Integrals in Cartesian Coordinates

 13.8 Triple Integrals in Cylindrical and Spherical Coordinates

 13.9 Change of Variables in Multiple Integrals

 13.10 Chapter Review

 Review and Preview Problems

14 Vector Calculus

 14.1 Vector Fields

 14.2 Line Integrals

 14.3 Independence of Path

 14.4 Green's Theorem in the Plane

 14.5 Surface Integrals

 14.6 Gauss's Divergence Theorem

 14.7 Stokes's Theorem

 14.8 Chapter Review

Appendix

 A.1 Mathematical Induction

 A.2 Proofs of Several Theorems

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