# Calculus: Early Transcendentals (3rd Edition)

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Book Preface

The third edition of Calculus: Early Transcendentals supports a three-semester or fourquarter calculus sequence typically taken by students studying mathematics, engineering, the natural sciences, or economics. The third edition has the same goals as the first edition:

• to motivate the essential ideas of calculus with a lively narrative, demonstrating the utility of calculus with applications in diverse fields;
• to introduce new topics through concrete examples, applications, and analogies, appealing to students’ intuition and geometric instincts to make calculus natural and believable; and
• once this intuitive foundation is established, to present generalizations and abstractions and to treat theoretical matters in a rigorous way. The third edition both builds on the success of the previous two editions and addresses the feedback we have received. We have listened to and learned from the instructors who used the text. They have given us wise guidance about how to make the third edition an even more effective learning tool for students and a more powerful resource for instructors. Users of the text continue to tell us that it mirrors the course they teach—and, more important, that students actually read it! Of course, the third edition also benefits from our own experiences using the text, as well as from our experiences teaching mathematics at diverse institutions over the past 30 years.

New to the Third Edition Exercises

The exercise sets are a major focus of the revision. In response to reviewer and instructor feedback, we’ve made some significant changes to the exercise sets by rearranging and relabeling exercises, modifying some exercises, and adding many new ones. Of the approximately 10,400 exercises appearing in this edition, 18% are new, and many of the exercises from the second edition were revised for this edition. We analyzed aggregated student usage and performance data from MyLab™ Math for the previous edition of this text. The results of this analysis helped us improve the quality and quantity of exercises that matter the most to instructors and students. We have also simplified the structure of the exercises sets from five parts to the following three:

1. Getting Started contains some of the former Review Questions but goes beyond those to include more conceptual exercises, along with new basic skills and short-answer exercises. Our goal in this section is to provide an excellent overall assessment of understanding of the key ideas of a section.

2. Practice Exercises consist primarily of exercises from the former Basic Skills, but they also include intermediate-level exercises from the former Further Explorations and Application sections. Unlike previous editions, these exercises are not necessarily organized into groups corresponding to specific examples. For instance, instead of separating out Product Rule exercises from Quotient Rule exercises in Section 3.4, we have merged these problems into one larger group of exercises. Consequently, specific instructions such as “Use the Product Rule to find the derivative of the following functions” and “Use the Quotient Rule to find the derivative of the given functions” have been replaced with the general instruction “Find the derivative of the following functions.” With Product Rule and Quotient Rule exercises mixed together, students must first choose the correct method for evaluating derivatives before solving the problems.

3. Explorations and Challenges consist of more challenging problems and those that extend the content of the section.

We no longer have a section of the exercises called “Applications,” but (somewhat ironically) in eliminating this section, we feel we are providing better coverage of applications because these exercises have been placed strategically throughout the exercise sets. Some are in Getting Started, most are in Practice Exercises, and some are in Explorations and Challenges. The applications nearly always have a boldface heading so that the topic of the application is readily apparent.

Regarding the boldface heads that precede exercises: These heads provide instructors with a quick way to discern the topic of a problem when creating assignments. We heard from users of earlier editions, however, that some of these heads provided too much guidance in how to solve a given problem. In this edition, therefore, we eliminated or reworded run-in heads that provided too much information about the solution method for a problem. Finally, the Chapter Review exercises received a major revamp to provide more exercises (particularly intermediate-level problems) and more opportunities for students to choose a strategy of solution. More than 26% of the Chapter Review exercises are new.