Brief Applied Calculus

Many of the book's contemporary and interesting applications use real, sourced data from a wide range of fields including athletics, biomedical sciences, environmental sciences, management science and business, personal finance and management, social and behavioral sciences, and topics of general interest. A globe icon identifies real-world examples.

Sourced exercises establish factual basis and enable further research.

Regression (modeling) exercises in Chapter 1 ask students to use calculators to fit equations to actual data, and illustrate the methods used to develop the models in applied exercises throughout the book. Students can also benefit from optional examples on linear regression, power regression, quadratic regression, and exponential regression.

The book presents substantial treatment of limits involving infinity, graphing rational functions, and elasticity of demand. In addition to these expanded applications, more challenging exercises are included as well as a complete proof of the Chain Rule based on Carathédory's definition of the derivative.

Brief Examples, located immediately to the right of the boxes that summarize results, illustrate and provide immediate reinforcement of the concepts.

Optional Graphing Calculator Explorations and exercises explore new topics, allow students to easily carry out otherwise messy calculations, or show the limitations and pitfalls of technology. To allow for optional use of the graphing calculator, the Calculator Explorations are boxed, and an icon identifies exercises that require a graphing calculator.

Spreadsheet Explorations are included for select chapters of the text for those who prefer Microsoft® Excel or other spreadsheet technology.

Chapter Summaries, organized by section, review key concepts and reference specific review exercises that allow students to check their understanding. Chapter-ending Hints and Suggestions offer special reminders of essential facts or "tricks" that students might otherwise overlook.

A Diagnostic Test has been added to help students identify skills that may need review. This test appears before Chapter 1.

An Algebra Review appears in an appendix, keyed to parts of the text, for additional reference.

New material on parallel and perpendicular lines has been added to Section 1.1, "Real Numbers, Inequalities, and Lines."

Section 3.7, "Differentials, Approximations, and Marginal Analysis," is new to the seventh edition. This section is optional and can be omitted without loss of continuity.

New exercises have been added and over 100 updated (including all of the Wall Street financial exercises) with current real-world data and accompanying sources. New "Explorations and Excursions" exercises give further details or theoretical underpinnings of the topics in the main narrative.