Higher Education

# Elementary Mathematical Modeling: A Dynamic Approach, 1st Edition

• James Sandefur Georgetown University
• ISBN-10: 053437803X  |  ISBN-13: 9780534378035
• 375 Pages
• College Bookstore Wholesale Price = \$200.50

### Overview

ELEMENTARY MATHEMATICAL MODELING uses mathematics to study problems arising in areas such as Genetics, Finance, Medicine, and Economics. Throughout the course of the book, students learn how to model a real situation, such as testing levels of lead in children or environmental cleanup. They then learn how to analyze that model in relationship to the real world, such as making recommendations for minimum treatment time for children exposed to lead paint or determining the minimum time required to adequately clean up a polluted lake. Often the results will be counterintuitive, such as finding that an increase in the rate of wild-life harvesting may actually decrease the long-term harvest, or that a lottery prize that is paid out over a number of years is worth far less than its advertised value. This use of mathematics illustrates and models real-world issues and questions, bringing the value of mathematics to life for students, enabling them to see, perhaps for the first time, the utility of mathematics.

1. INTRODUCTION TO MODELING.
Introduction to Dynamical Systems. Examples of Modeling. Affine Dynamical Systems. Parameters. Financial Models.
2. ANALYSIS OF DYNAMICAL SYSTEMS.
Introduction to Analysis. Equilibrium. Stability. Ratios and Proportional Change. Stable Distributions. Cycles.
3. FUNCTION APPROACH.
Introduction to Function Approach. Linear Functions. Exponential Functions. Exponential Growth Decay.
Translations of Exponential Functions. Curve Fitting.
4. HIGHER ORDER DYNAMICAL SYSTEMS.
Introduction. Counting Sets. Introduction to Probability. The Gambler's Ruin. Analyzing Higher Order Dynamical Systems. An Economic Model. Controlling an Economy. Exponential and Trigonometric Functions.
5. NONLINEAR DYNAMICAL SYSTEMS.
Introduction. The Dynamics of Alcohol. Stability. Web Analysis.
6. POPULATION DYNAMICS.
Introduction to Population Growth. The Logistic Model for Population Growth. Nonlinear Growth Rates. Graphical Approach to Harvesting. Analytic Approach to Harvesting. Economics of Harvesting.
7. GENETICS.
Introduction to Population Genetics. Basics of Genetics. Mutation. Selection.

## Efficacy and Outcomes

### Reviews

"Teaching math to "not-necessarily-too-interested" students requires a combination of excellent motivation and accessible techniques. This text appears to do well on both fronts. I am delighted with the applications; they are relevant, highly motivational and presented at the right level."

— Charles Doering, University of Michigan

"The interpretation of mathematics results in terms of applications is top rate. I can envision them instigating excellent and thought provoking discussions."

— Charles Doering, University of Michigan

"Teaching a course at this level always requires a subtle balance between how much one wants to get into an how many practical problems one can solve with sufficiently quantitative conclusions and with a broad intellectual appeal to students....Sandefurâ€™s text has achieved this balance well."

— David Chi, University of North Carolina - Chapel Hill

"...the most significant challenge in teaching this course (is) a potentially very diverse range of mathematical backgrounds, and perhaps dealing with students who are nor entirely enthusiastic about math and science. I believe (Sandefur)would be effective in such a situation. I say this because the book is not about learning more mathematics but about learning to use and apply the mathematics that one already knows. I believe the mathematical level would be accessible to even the most diverse group of students, and the applications would be of interest to them as well."

— Oscar Gonzalez, University of Texas - Austin

## Meet the Author

### James Sandefur

Dr. James Sandefur received his Ph.D. in Mathematics from Tulane University and is Professor of Mathematics at Georgetown University. His interests are in differential equations in Hilbert space, equipartition of energy, and discrete dynamical systems. He has written nearly 40 mathematics papers and is the author of the texts "Discrete Dynamical Systems: Theory and Applications" and "Discrete Dynamical Modeling". He was the Principal Investigator on three different NSF grants, a Teacher Enhancement Institute, a Teacher Leadership Grant, and the Curriculum Development Grant, Hands-on Activities for Algebra, to develop hands-on models for developmental college math courses. He is a writer for the NCTM's Principles and Standards . Dr. Sandefur was a program officer at NSF in the Instructional Materials Development Program. He has been a Visiting Professor at the Cornell University Center for Applied Mathematics, the University of Iowa, and the Freudenthal Institute at the University of Utrecht. Jim developed this manuscript for his freshmen-level modeling course for non-science majors at Georgetown. His course consistently fills and often has a waiting list, because of its popularity.