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Elementary Mathematical Modeling : A Dynamic Approach: A dynamic approach

Elementary Mathematical Modeling : A Dynamic Approach: A dynamic approach


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About the Book

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.

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.

About the Author :
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.

Review :
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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Product Details
  • ISBN-13: 9780534378035
  • Publisher: Cengage Learning, Inc
  • Publisher Imprint: Brooks/Cole
  • Edition: New edition
  • Returnable: N
  • ISBN-10: 053437803X
  • Publisher Date: 11 Nov 2002
  • Binding: Hardback
  • Language: English
  • Sub Title: A dynamic approach


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