Elementary Mathematical Modeling : Functions and Graphs

by Davis, Mary Ellen; Edwards, C. Henry

• ISBN13: 9780130962027
• ISBN10: 0130962023
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: PRENTICE HALL

Summary

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.

Table of Contents

(NOTE: Each chapter concludes with a Review.)
1. Linear Functions and Models.

Functions and Mathematical Modeling. Linear Functions and Graphs. Constant Change and Linear Growth. Fitting Linear Models to Data.

2. Quadratic Functions and Models.

Quadratic Functions and Polynomials. Quadratic Models and Equations. Fitting Quadratic Models to Data.

3. Natural Growth Models.

Percentage Growth and Interest. Solving Growth Problems with Tables and Graphs. Natural Growth and Decline in the World. Fitting Natural Growth Models to Data.

4. Exponential and Logarithmic Models.

Compound Interest and Exponential Functions. Exponential and Logarithmic Functions. Exponential and Logarithmic Data Modeling.

5. Polynomial Models and Linear Systems.

Solving Polynomial Equations. Solving Pairs of Linear Equations—Lots of Ways! Linear Systems of Equations. Polynomial Data Modeling.

6. Trigonometric Models.

Periodic Phenomena and Trigonometric Functions. Trigonometric Models and Periodic Data.

7. Bounded Growth Models.

Limited Populations. Fitting Logistic Models to Data. Discrete Models and Chaos.

8. Optimization.

Highs and Lows. Applied Maxima and Minima I. Applied Maxima and Minima II.

Answers to Selected Problems.
Index.
Credits.

Excerpts

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