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**Applied Calculus, 6th Edition**

**Applied Calculus, 6th Edition**

**ISBN-13:**978-1119408901

**ISBN-10:**1119408903

Interactive classrooms and well-crafted problems promote student learning. Since it’s inception, the hallmark of * Applied Calculus* is its innovative and engaging problems. The Calculus Consortium pioneered and incorporates the approach called the “Rule of Four.” The Rule of Four, presents ideas graphically, numerically, symbolically, and verbally, thereby encouraging students with a variety of learning styles to deepen their understanding as they work through a wide variety of problem types.

To Students: How to Learn from this Book

- This book may be different from other math textbooks that you have used, so it may be helpful to know about some of the differences in advance. At every stage, this book emphasizes the meaning (in practical, graphical or numerical terms) of the symbols you are using. There is much less emphasis on “plug-andchug” and using formulas, and much more emphasis on the interpretation of these formulas than you may expect. You will often be asked to explain your ideas in words or to explain an answer using graphs.
- The book contains the main ideas of calculus in plain English. Success in using this book will depend on reading, questioning, and thinking hard about the ideas presented. It will be helpful to read the text in detail, not just the worked examples.
- There are few examples in the text that are exactly like the homework problems, so homework problems can’t be done by searching for similar–looking “worked out” examples. Success with the homework will come by grappling with the ideas of calculus.
- For many problems in the book, there is more than one correct approach and more than one correct solution. Sometimes, solving a problem relies on common sense ideas that are not stated in the problem explicitly but which you know from everyday life.
- Some problems in this book assume that you have access to a graphing calculator or computer. There are many situations where you may not be able to find an exact solution to a problem, but you can use a calculator or computer to get a reasonable approximation.
- This book attempts to give equal weight to four methods for describing functions: graphical (a picture), numerical (a table of values), algebraic (a formula), and verbal (words). Sometimes it’s easier to translate a problem given in one form into another. For example, you might replace the graph of a parabola with its equation, or plot a table of values to see its behavior. It is important to be flexible about your approach: if one way of looking at a problem doesn’t work, try another.
- Students using this book have found discussing these problems in small groups helpful. There are a great many problems which are not cut-and-dried; it can help to attack them with the other perspectives your colleagues can provide. If group work is not feasible, see if your instructor can organize a discussion session in which additional problems can be worked on.
- You are probably wondering what you’ll get from the book. The answer is, if you put in a solid effort, you will get a real understanding of one of the crowning achievements of human creativity—calculus— as well as a real sense of the power of mathematics in the age of technology.

**Preface**

Calculus is one of the greatest achievements of the human intellect. Inspired by problems in astronomy, Newton and Leibniz developed the ideas of calculus 300 years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathematics, the physical sciences, engineering, business, and the social and biological sciences.

Calculus has been so successful because of its extraordinary power to reduce complicated problems to simple rules and procedures. Therein lies the danger in teaching calculus: it is possible to teach the subject as nothing but the rules and procedures—thereby losing sight of both the mathematics and of its practical value.

This edition of Applied Calculus continues our effort to promote courses in which understanding reinforces computation.

Embracing e-Learning

Paper books are playing a smaller role in courses than in the past and are being replaced by electronic materials. This Sixth Edition provides opportunities for students to experience the concepts of calculus in ways that would not be possible in a traditional textbook. The enhanced e-text of Applied Calculus, powered by VitalSource, provides embedded videos and the complete solutions from the Student Solutions Manual. The enhanced e-text also contains additional content not found in the print edition:

• Worked example videos, which provide students the opportunity to see and hear over one hundred of the book’s examples being explained and worked out in detail, have been created to accompany the sixth

edition.

• Strengthen Your Understanding true/false problems that focus on conceptual understanding.

• Appendices that extend ideas in the course.

• Chapter 10, on Geometric Series.

• Chapter summaries, giving a concise overview of each chapter.

WileyPLUS

In addtion to the enhanced e-text, Students and instructors can access a wide variety of rescources through WileyPLUS with ORION, Wiley’s digital learning environment. ORION Learning provides an adaptive, personalized learning experience that delivers easy-to-use analytics so instructors and students can see exactly where they’re excelling and where they need help. WileyPLUS with ORION features the following resources:

• Homework management tools, which enable the instructor to assign questions easily and grade them automatically, using a rich set of options and controls.

• QuickStart pre-designed reading and homework assignments. Use them as-is or customize them to fit the needs of your classroom.

• Intelligent Tutoring questions, in which students are prompted for responses as they step through a problem solution and receive targeted feedback based on those responses.

• Algebra Refresher material, delivered through ORION, provides students with an opportunity to brush up on material necessary to master Calculus, as well as to determine areas that require further review.

• Graphing Calculator Manual, to help students get the most out of their graphing calculator, and to show how they can apply the numerical and graphing functions of their calculators to their study of calculus.

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