微积分

出版说明

序

Preface

0 Preliminaries

0.1 Real Numbe.Estimation，and Logic

0.2 Inequalities and Absolute Values

0.3 The Rectangular Coordinate System

0.4 Graphs of Equatio

0.5 Functio and Their Graphs

0.6 Operatio on Functio

0.7 Trigonometric Functio

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 Functio

1.5 Limits at Infinity；Infinite Limits

1.6Continuity of Functio

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 Functio

2.5 The Chain Rule

2.6 Higher.Order Derivatives

2.7 Implicit Differentiation

2.8 Related Rates

2.9 Differentials and Approximatio

2.10 Chapter Review

Review and Preview Problems

3 Applicatio 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 Functio Using Calculus

3.6 The Mean Value Theorem for Derivatives

3.7 Solving Equatio Numerically

3.8 Antiderivatives

3.9 Introduction to Differential Equatio

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 Fit 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 Applicatio of the Integral

5.1 The Area of a Plane Region

5.2 volumes of Solids：Slabs.Disks,Wlashe

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 Tracendental Functio

6.1 The Natural Logarithm Function

6.2 Invee Functio and Their Derivatives

6.3 The Natural Exponential Function

6.4 General Exponential and Logarithmic Functio

6.5 Exponential Growth and Decay

6.6 Fit.Order Linear Differential Equatio

6.7 Approximatio for Differential Equatio

6.8 The Invee Trigonometric Functio and Their Derivatives

6.9 The Hyperbolic Functio and Their Invees

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 Substitutio

7.5 Integration of Rational Functio Using Partial Fractio

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 Operatio 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 Tralation and Rotation of Axes

10.4 Parametric Representation of Curves in the Plane

10.5 The Polar Coordinate System

10.6 Graphs of Polar Equatio

10.7 Calculus in Polar Coordinates

10.8 Chapter Review

Review and Preview Problems

11 Geometry in Space and Vecto

11.1 Cartesian Coordinates in Three-Space

11.2 Vecto

11.3 The Dot Product

11.4 The Cross Product

11.5 Vector-Valued Functio 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 Functio of Two or More Variables

12.1 Functio 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 Approximatio

12.8 Maxima and Minima

12.9 The Method of Lagrange Multiplie

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 Regio

13.4 Double Integrals in Polar Coordinates

13.5 Applicatio 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

教辅材料说明

教辅材料申请表

《微积分（英文版·原书第9版）》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，《微积分(英文版·原书第9版)》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。
　　《微积分（英文版·原书第9版）》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。