Discrete Dynamical Modeling

Hardcover | April 1, 1995

byJames T. Sandefur

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This book presents an introduction to the wide range of techniques and applications for dynamic mathematical modeling that are useful in studying systemic change over time. The author expertly explains how the key to studying change is to determine a relationship between occurring events andevents that transpire in the near future. Mathematical modeling of such cause-and-effect relationships can often lead to accurate predictions of events that occur farther in the future. Sandefur's approach uses many examples from algebra--such as factoring, exponentials and logarithms--and includesmany interesting applications, such as amortization of loans, balances in savings accounts, growth of populations, optimal harvesting strategies, genetic selection and mutation, and economic models. This book will be invaluable to students seeking to apply dynamic modeling to any field in whichchange is observed, and will encourage them to develop a different way of thinking about the world of mathematics.

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This book presents an introduction to the wide range of techniques and applications for dynamic mathematical modeling that are useful in studying systemic change over time. The author expertly explains how the key to studying change is to determine a relationship between occurring events andevents that transpire in the near future. Ma...

James T. Sandefur is at Georgetown University.

other books by James T. Sandefur

Format:HardcoverDimensions:448 pages, 6.46 × 9.49 × 1.42 inPublished:April 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195084381

ISBN - 13:9780195084382

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Table of Contents

1. Introduction to Dynamic Modeling1.1. Modeling Drugs in the Bloodstream1.2. Terminology1.3. Equilibrium Values1.4. Dynamic Economic Applications1.5. Applications of Dynamics Using Spreadsheets2. First Order Dynamical Systems2.1. Solutions to Linear Dynamical Systems with Applications2.2. Solutions to an Affine Dynamical System2.3. An Introduction to Genetics2.4. Solutions to Affine Dynamical Systems with Applications2.5. Application to Finance3. Introduction to Probability3.1. The Multiplication and Addition Principles3.2. Introduction to Probability3.3. Multistage Tasks3.4. An Introduction to Markov Chains4. Nonhomogeneous Dynamical Systems4.1. Exponential Terms4.2. Exponential Terms, a Special Case4.3. Fractal Geometry4.4. Polynomial Terms4.5. Polynomial Terms, a Special Case5. Higher Order Linear Dynamical Systems5.1. An Introduction to Second Order Linear Equations5.2. Multiple Roots5.3. The Gambler's Ruin5.4. Sex-Linked Genes5.5. Stability for Second Order Affine Equations5.6. Modeling a Vibrating String5.7. Second Order Nonhomogeneous Equations5.8. Gambler's Ruin Revisited5.9. A Model of a National Economy5.10. Dynamical Systems with Order Greater than Two5.11. Solutions Involving Trigonometric Functions6. Introduction to Nonlinear Dynamical Systems6.1. A Model of Population Growth6.2. Using Linearization to Study Stability6.3. Harvesting Strategies6.4. More Linearization7. Vectors and Matrices7.1. Introduction to Vectors and Matrices7.2. Rules of Linear Algebra7.3. Gauss-Jordan Elimination7.4. Determinants7.5. Inverse Matrices8. Dynamical Systems of Several Equations8.1. introduction to Dynamical Systems of Several Equations8.2. Characteristic Values8.3. First Order Dynamical Systems of Several Equations8.4. Regular Markov Chains8.5. Absorbing Markov Chains8.6. Applications of Absorbing Markov Chains8.7. Long Term Behavior of Solutions8.8. The Heat Equation

Editorial Reviews

"A closely related textbook by the same author [Discrete Matematical Systems] was reviewed here previously....Modeling is more self-contained than Systems, in that it includes sections on elementary counting and probability and a short chapter on vectors and matrices (which are used in thefinal chapter to study dynamical systems of several linear equations). It also has new sections on elementary fractal geometry and on using spreadsheets to explore dynamical systems empirically. The latter section is especially well-written and could serve as an effective and entertaining tutorialon the use of spreadsheet software....Modeling could be a good choice for-to take an example-an honors course in dynamics at the high-school level. The exposition in both texts is outstanding....I hope that they both remain available in the future." --The UMAP Journal-The Journal of UndergraduateMathematics and Its Applications