Elementary Mathematical Modeling: Functions and Graphs - Hardcover

Mary Ellen Davis

Hardcover

ISBN 10: 0130962023 ISBN 13: 9780130962027

Publisher: Prentice Hall, 2000

Synopsis

This book helps readers develop the quantitative literacy skills and savvy needed to function effectively in society and the workplace. It focuses on "mathematical modeling" and the use of elementary mathematics--e.g., numbers and measurement, algebra, geometry, and data exploration--to investigate real-world problems and questions. It assumes no technology other than the use of graphing calculators, and provides a comprehensive technology support system on an accompanying CD-ROM and web site. Linear Functions and Models. Quadratic Functions and Models. Natural Growth Models. Exponential and Trigonometric Models. Polynomial Models and Linear Systems. Optimization Problems. Bounded Growth Models. For anyone wanting to develop proficiency in mathematical modeling.

About this title

About the Author

MARY ELLEN DAVIS Georgia Perimeter College, received her Master of Arts degree in mathematics from the University of Missouri-Columbia in 1976. She has taught mathematics at the secondary level and at Georgia State University and the University of Birmingham (England). She joined the mathematics department at Georgia Perimeter College (then DeKalb College) in 1991 and has taught a wide range of courses from college algebra to calculus and statistics. She was instrumental in the piloting and implementing of the college's Introduction to Mathematical Modeling course in 1998. She was selected as a Georgia Governor's Teaching Fellow in 1996, and in 1999 received a GPC Distance Education Fellowship to develop web-based materials for applied calculus.

C. HENRY EDWARDS (Ph.D. University of Tennessee) Emeritus professor of mathematics at the University of Georgia, Edwards recently retired after 40 years of undergraduate classroom teaching at the universities of Tennessee, Wisconsin, and Georgia. Although respected for his diverse research interests, Edwards' first love has always remained teaching. Throughout his teaching career he has received numerous college- and university-wide teaching awards, including the University of Georgia's honoratus medal in 1983 and its Josiah Meigs award in 1991. In 1997, Edwards was the first university-level faculty recipient of the Georgia Board of Regents newly-instituted state-wide award for teaching excellence.

A prolific author, Edwards is co-author of well-known calculus and differential equations textbooks and has written a book on the history of mathematics, in addition to several instructional computer manuals. During the 1990s, Edwards has worked on three NSF-supported projects that fostered a better integration of technology into the mathematics curriculum. The last three years of his long teaching career were devoted principally to the development of a new technology-intensive entry-level mathematics course on which this new textbook is based. Additional information is provided on his web page www.math.uga.edu/~hedwards.

From the Inside Flap

PREFACE

This textbook is for an entry-level college mathematics course at the same academic level as college algebra, but intended for students who are not necessarily preparing for subsequent courses in calculus. Our approach is based on the exploitation of graphing-calculator technology to engage students in concrete modeling applications of mathematics. The mathematical ideas of the course center on functions and their graphs—ranging from linear functions and polynomials to exponential and trigonometric functions—that we hope will seem familiar and friendly to students who complete the course. BRIEF DESCRIPTION

Specifically, this textbook presents an introduction to mathematical modeling based on the use of elementary functions to describe and explore real-world data and phenomena. It demonstrates graphical, numerical, symbolic, and verbal approaches to the investigation of data, functions, equations, and models. We emphasize interesting applications of elementary mathematics together with the ability to construct useful mathematical models, to analyze them critically, and to communicate quantitative concepts effectively. In short, this is a textbook for

A graphing technology intensive course that is An alternative to the standard college algebra course, and is Solidly based on functions, graphs, and data modeling. RATIONALE FOR A NEW COURSE

The content of the traditional college algebra course is defined largely by the paper-and-pencil skills (mainly symbolic manipulation) that are needed by students whose curricula point them towards a subsequent calculus course. However, many of the students in a typical college algebra course are not really headed for calculus or never make it there. For too many of these students, college algebra consists of revisiting the skills and concepts, either mastered or not, which were "covered" in several previous mathematics courses. This experience leaves students with little enhancement of the quantitative skills they most need for their subsequent studies. It is a missed opportunity for them to begin college with a useful mathematics course that is interesting both to students and to instructors, and which offers a solid chance for progress and success.

There is wide agreement on the need for an alternative new approach to fill this void. Both the NCTM's Principles and Standards for School Mathematics and AMATYC's Crossroads in Mathematics: Standards for Introductory College Mathematics Before Calculus recommend that mathematics courses teach students to reason mathematically, to model real-world situations, and to make use of appropriate technologies. We offer this as an appropriate textbook for such a course. The evolution of these materials began with a web site that was originally developed (starting in 1996) to support University of Georgia students taking pilot sections of this new course. About two thousand students have now used preliminary versions of the textbook. Many of these students have reacted with enthusiasm belying their typical lack of success in prior mathematical experiences. We hope this apparent success and satisfaction will carry over to the students who use this published textbook. PURPOSE AND OBJECTIVES

The primary objective of this new course is the development of the quantitative literacy and savvy that college graduates need to function effectively in society and workplace. The course exploits technology and real-world applications to motivate necessary skill development and the ability to reason and communicate mathematically, to use elementary mathematics to solve applied problems, and to make connections between mathematics and the surrounding world.

With a flavor combining functions and graphs with data modeling, the course is based largely on the use of graphing calculator methods in lieu of traditional symbolic manipulations to solve both familiar and nonstandard problems. The focus of the course is "mathematical modeling" and the use of elementary mathematics—numbers and measurement, algebra, geometry, and data exploration—to investigate real-world problems and questions.

As an alternative to the standard college algebra course—though at the same academic level—this course is intended for students who are not necessarily headed for calculus-based curricula, but still need a solid quantitative foundation both for subsequent studies and for life as educated citizens and workers. Graphing technology enables these students to experience the power of mathematics and to enjoy success in solving interesting and significant problems (an experience that they all too rarely enjoy in traditional college algebra courses). PURPOSE AND OBJECTIVES

The book consists of the following chapters:

Linear Functions and Models Quadratic Functions and Models Natural Growth Models Exponential and Logarithmic Models Polynomial Models and Linear Systems Trigonometric Models Bounded Growth Models Optimization

Edition details

• Publisher: Prentice Hall
• Publication date: 2000
• ISBN 10: 0130962023
• ISBN 13: 9780130962027
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 600