The first edition was intended to be a synthesis of reform and traditional approaches to calculus instruction.In this second edition I continue to follow that path by empha-sizing conceptual understanding through visual,numerical,and algebraic approaches.The principal way in which this book differs from my more traditional calculus textbooks is that it is more streamlined. For instance,there is no complete chapter on techniques of integration;I don't prove as many theorems;and the material on transcendental functions and on parametric equations is interwoven throughout the book instead of being treated in separate chapters.Instruc-tors who prefer fuller coverage of traditional calculus topics should look at my books Calculus,Fourth Edition and Calculus: Early Transcendentals,Fourth Edition.

A Preview of Calculus

1 Functions and Models

　1.1 Four Ways to Represent a Function

　1.2 Mathematical Models

　1.3 New Functions from Old Functions

　1.4 Graphing Calculators and Computers

　1.5 Exponential Functions

　1.6 Inverse Functions and Logarithms

　1.7 Parametric Curves

　Laboratory Project Running Circles around Circles

　Review

　Principles of Problem Solving

2 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 Continuity

　2.5 Limits Involving Infinity

　2.6 Tangents, Velocities, and Other Rates of Change

　2.7 Derivatives

　Writing Project: Early Methods for Finding Tangents

　2.8 The Derivative as a Function

　2.9 Linear Approximations

　2.10 What Does f1 Say about f?

　Review

　Focus on Problem Solving

3 Differentiation Rules

4 Applications of Differentiation

5 Integrals

6 Applications of Integration

7 Differential Equations

8 Infinite Sequences and Series

9 Vectors and the Geometry of Space

10 Vector Functions

11 Partial Derivatives

12 Multiple Integrals

13 Vector Calculus

Appendixes

Index