微积分

Preface xi

To the Student xxiii

Diagnostic Tests xxiv

A PREVIEW OF CALCULUS

Functions and Models

1.1 Four Ways to Represent a Function

1.2 Mathematical Models： A Catalog of Essential Functions

1.3 New Functions from Old Functions

1.4 Graphing Calculators and Computers

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms Review

Principles of Problem Solving

Limits and Derivatives

2.1 The Tangent and Velocity Problems

2.2 The Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 The Precise Definition of a Limit

2.5 Continuity

2.6 Limits at Infinity; Horizontal Asymptotes

2.7 Derivatives and Rates of Change 143

Writing Project - Early Methods for Finding Tangents

2.8 The Derivative as a Function

Review

Problems Plus

3 Differentiation Rules

4 Applications of Differentiation

5 Integrals

6 Applications of Integration

7 Techniques of Integration

8 Further Applications of Integration

9 Differential Equations

10 Parametric Equations and Polar Coordinates

11 Infinite Sequences and Series

12 Vectors and the Geometry of Space

13 Vector Functions

14 Partial Derivatives

15 Multiple Integrals

16 Vector Calculus

17 Second-Order Differential Equations

Appendixes

Index

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