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Chapter Openers

Each chapter opens with a photograph that corresponds to the mathematical application in Motivating the Chapter.

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Motivating the Chapter

Each Motivating the Chapter explores the concepts to be covered in the chapter using a real-world setting. Following a short introduction, open-ended questions guide students through an introduction to the main themes of the chapter.

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Section Topics

Each section begins with a list of subsection topics. This outline will help instructors with class planning and help students with studying and synthesizing the material in the section.

Explorations

Before students are exposed to selected topics, exploratory projects allow them to discover concepts on their own, making them more likely to remember the results. These optional boxed features can be omitted, if the instructor so desires, with no loss of continuity in the coverage of material.

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Examples

To increase the usefulness of the text as a study tool, the Sixth Edition contains over 1000 examples, each titled for easy reference. Many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically to provide further insight into mathematical concepts. Side comments clarify the steps of the solution as necessary.

Graphics

The Sixth Edition has over 3500 figures. Computer-generated for accuracy, clarity, and realism, this new art program will help students visualize mathematical concepts more easily. The surfaces and solids of complex, three-dimensional figures were created using the optimal combination of color and transparency, view, perspective, light sources, and shadows to show true perspective.

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Summaries

Many sections have summaries that identify core ideas and procedures. In some instances, an entire section summarizes the preceding topics.

Definitions and Theorems

All definitions and theorems are highlighted for emphasis and easy reference.

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Technology

Students are encouraged to use a graphing utility or computer algebra system as a tool for exploration, discovery, and problem solving. Many opportunities to execute complicated computations, to visualize theoretical concepts, to discover alternative approaches, and to verify the results of other solution methods using technology are presented. However, students are not required to have access to a graphing utility to use this text effectively. In addition to describing the benefits of using technology, the text also pays special attention to its possible misuse or misinterpretation.

Historical Notes

Historical notes are integrated throughout the text to help students understand that calculus has a past.

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Notes

Many instructional notes accompany definitions, theorems, and examples to give additional insight or describe generalizations.

Study Tips

Throughout the text, Study Tips help students avoid common errors, address special cases, and expand on theoretical concepts.

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Exercises

The text contains nearly 10,000 exercises. Each exercise set is graded, progressing from skill-development problems to more challenging problems involving applications and proofs. The wide variety of exercises includes many real, technology-oriented, thought-provoking, and engaging problems. Review exercises are included at the end of each chapter. Answers to all odd-numbered exercises are included in the back of the text. Red (blue, in the appendix) exercise numbers indicate selected exercises that can be found in the Study and Solutions Guide. To help instructors make homework assignments, many of the exercises in the text are labeled to indicate the area of application (e.g., Break-Even Point) or the type of exercise (e.g., Writing or Approximation).

Lab Series

The real-life application introduced in each Motivating the Chapter forms the basis for extended lab projects in the supplementary Lab Manuals using Maple, Mathematica, Derive, Mathcad, and the TI-92 graphing calculator. The labs are referenced in the text where it seemed most appropriate to assign them.

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Think About It

These exercises are thought-provoking, conceptual problems that help students grasp the underlying theories.

Applications

A wide variety of relevant application problems are included to demonstrate clearly the real-world usage of mathematics.

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Modeling Data

These new multipart questions ask students to find and interpret mathematical models from real-life data. Often the questions are enhanced by the use of a graphing utility.

Section Projects

New to the Sixth Edition, Section Projects appear at the end of selected exercise sets. These extended applications can be assigned to individual students or to groups of students in a peer-assisted learning environment.

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Writing

To develop students' reasoning skills and make them comfortable discussing mathematical concepts, the text now contains many Writing exercises.

Graphing Utilities

Many exercises in the text can be solved using technology; however, the symbol identifies all exercises in which students are specifically instructed to use a graphing utility or a computer algebra system.

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True or False?

To help students understand the logical structure of calculus, a set of "true or false" questions is included toward the ends of many exercise sets. These questions help students focus on concepts, common errors, and the correct statements of definitions and theorems.

Journal References

References to articles in readily available journals help students understand that calculus is a current, dynamic field.

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