Preface

Applied Calculus: A Graphing Approach is a one-semester, technology-required, reform calculus book for students majoring in business, economics, life sciences, and social sciences. The text places considerable emphasis on translating back and forth among graphs, formulas, numbers, and words. Prime importance is given to understanding the meaning of the first and second derivatives and the integral, especially with regard to applications. Technology is used to gain insights into the fundamental concepts of calculus.

## HOW DOES THIS BOOK DIFFER FROM OTHER "APPLIED CALCULUS"BOOKS?

TECHNOLOGY REQUIRED Students are expected to use a graphing calculator or a computer with mathematical software. Individual instructors can determine the balance between technology and symbol manipulation. For instance, students can solve the consumers' surplus problem by evaluating the definite integral with a calculator, with the fundamental theorem of calculus, or with both.

GRAPHICAL EMPHASIS Although students are expected to sketch simple graphs by hand, they will rely on graphing utilities for creating most graphs. The effort saved is put into learning to read and interpret graphs. Also, the text has more graphs than the average applied calculus text.

FUNDAMENTAL CONCEPTS GIVEN PRIORITY OVER SYMBOL MANIPULATION The concept of the derivative is discussed extensively in Chapter 2, whereas symbolic differentiation is postponed until Chapter 3. Applications of the definite integral precede the fundamental theorem of calculus. Students with weak algebraic skills do get an opportunity to improve their skills; however, the lack of algebraic skills should not hinder their understanding of the important concepts of calculus. Instructors can decide how much algebraic manipulation to require.

The book stays focused on its main objectives--understanding the meaning of the first and second derivatives and the integral, especially within the context of applications. (Graphing tricky functions, mastering every nuance of using graphing calculators, and doing complicated calculations are not objectives.) The book presents in detail the significance of the derivative before it asks the student to calculate derivatives algebraically. Also, it presents the meaning and wide variety of uses of the integral before giving the fundamental theorem of calculus. Key applications are examined several times in the text, each time from a slightly different viewpoint.

## WHY DOES THE BOOK REFER SPECIFICALLY TO TI CALCULATORS AND VISUAL CALCULUS?

TI CALCULATORS If the book were written generically to apply to all graphing calculators, everyone would have to make adjustments. Since the TI-82, TI-83, and TI-85 calculators are the overwhelming favorite graphing calculators for calculus courses, nearly all students will have a book customized to their calculator. Section 1.2 presents the basic tasks to be performed, and other specialized tasks are discussed as needed. Appendices C, D, and E provide straightforward step-by- step summaries of using, respectively, the TI-82, TI-83, and TI-85.

VISUAL CALCULUS This software is the easiest-to-use calculus software available and is customized to the text. (About 500 functions from the text have been be entered into the software.) Appendix A explains how to use Visual Calculus. Colleges adopting the text will receive a free site license. In addition, the student study guide contains a copy of Visual Calculus.

Most students primarily will be using calculators. However, many of them also will have access to a computer. These students can use Visual Calculus to enhance the visualization, and therefore the understanding, of the fundamental concepts of calculus.

## HOW DOES THE BOOK MANAGE TO PROVIDE SO MUCH FL Updated Mar 11, 1998EXIBILITY TO THE INSTRUCTOR?

GENEROUS EXERCISE SETS The ample supply of exercises include traditional drill problems, problems that test understanding, and problems requiring technology. Instructors can choose the balance of exercises they feel is most suitable.

ABUNDANCE OF TOPICS The book contains more than a semester's worth of material. Therefore, instructors can tailor the course to the needs and interests of their students.

## WHAT ARE SOME OTHER SPECIAL FEATURES OF THE BOOK?

PRACTICE PROBLEMS FOR EACH SECTION The practice problems are carefully selected exercises located at the end of each section, just before the exercise set. Complete solutions are given following the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader seriously attempt the practice problems and study their solutions before moving on to the exercises. In effect, the practice problems constitute a built-in workbook.

CONCEPTUAL EXERCISES FOR EACH CHAPTER Each chapter ends with a set of exercises that review the fundamental concepts of the chapter. Many of these exercises require verbalization.

David I. Schneider
dis@math.umd.edu

David C. Lay

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