Elementary Mathematical Modeling: A Dynamic Approach / Edition 1

Elementary Mathematical Modeling: A Dynamic Approach / Edition 1

by James Sandefur
     
 

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ISBN-10: 053437803X

ISBN-13: 9780534378035

Pub. Date: 11/11/2002

Publisher: Cengage Learning

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,

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.

Product Details

ISBN-13:
9780534378035
Publisher:
Cengage Learning
Publication date:
11/11/2002
Edition description:
New Edition
Pages:
432
Product dimensions:
8.04(w) x 9.34(h) x 0.66(d)

Table of Contents

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. Answers to Odd Exercises.

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