About this Book

Last update: 5/9/14

The first edition of this text was published in 1996 by Houghton-Mifflin (with D. C. Heath imprint), a product of the NSF-supported Project CALC effort at Duke University. At that time we wrote:

Calculus is the study of change. The concepts of calculus enable us to model processes that change and to describe properties of these processes that remain constant in the midst of change. Now change has come to the learning of calculus — change driven by the need to respond to the revolution in technology and by our increased awareness of how students learn. This text is an outgrowth of and an agent of that change.

In our development of the course and the text we were guided by the following goals:

• Students should be able to use mathematics to structure their understanding of and investigate questions in the world around them.
• Students should be able to use calculus to formulate problems, to solve problems, and to communicate their solutions of problems to others.
• Students should be able to use technology as an integral part of this process of formulation, solution, and communication.
• Students should work and learn cooperatively.

These are still our goals. Now, with advances in technology, we are in a position to realize our aim of integrating text and student activities, both with and without technology, into a unified whole. These online course materials, centered on an online textbook, represent our continuing effort to do this.

The second edition continues to emphasize

• real-world problems,
• hands-on activities,
• discovery learning,
• writing and revision of writing,
• teamwork,
• intelligent use of available tools,
• high expectations of students, and
• students checking their own work.

Real-world contexts   We provide a real-world setting for each concept and calculational rule. For example, both differentiation and the exponential function appear early in Chapter 2 in connection with natural growth of populations. The Chain Rule is introduced as part of the modeling process for reflection and refraction of light. Both improper integrals and polynomial approximation of functions result from an investigation of models for the distribution of data. Throughout, we emphasize differential equations and initial value problems — the main connection between calculus and applications in the sciences and engineering.

Discovery learning   There are three features in the book that enhance discovery learning: Activities, Checkpoints, and standard Examples. We encourage students to construct their own knowledge by attempting Activities embedded in the text. These activities invite students to explore new concepts and problems, to see what the issues are before they are discussed in detail in the text. Each of these activities is supported by a discussion that leads into the new ideas. In addition, we encourage students to check their understanding by attempting Checkpoint calculations. These appear after the appropriate new ideas have been introduced; answers to most of these are provided in popup windows. The combination of Activities, Checkpoints, and Examples provides a wealth of engaging illustrations of the central concepts and techniques.

Problem solving   Throughout the text we emphasize general principles and practice in problem solving. At the end of each section we have provided a range of exercises, from practice calculations to additional development of concepts. The exercises are intended primarily for individual students, although the more challenging ones also work well for group activities in or out of class. In addition, each chapter has (or will have) a number of projects. These are more open-ended explorations designed for investigation by small groups of three or four students. They may be used in a variety of ways — for in-class activities that are written up in homework style or as a basis for more formal reports.

Technology   We assume each student has Internet access with s standards-compliant browser, such as Firefox or Safari.