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Discrete Dynamical Modeling - James T. Sandefur

Discrete Dynamical Modeling


Published: 1st June 1993
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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 and events 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 includes many 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 which change is observed, and will encourage them to develop a different way of thinking about the world of mathematics.

"A very nice book! It assumes minimal mathematical preparation and nevertheless arrives at very interesting and sophisticated results."--Maurice Kreevoy, University of Minnesota "Suitable for general audiences....Excellent examples and problems from many areas." --American Mathematical Monthly "The material presented in this textbook will help the reader apply discrete dynamics to many fields, such as business, economics, biology, genetics, engineering, and physics....[Sandefur] supplies interesting problems in all chapters; the answers to all even-numbered problems are given in the text. This book can serve as a valuable tool for researchers developing dynamic models." --Computing 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 the final 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 tutorial on 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 Undergraduate Mathematics and Its Applications

1: Introduction to Dynamic Modeling 1.1: Modeling Drugs in the Bloodstream 1.2: Terminology 1.3: Equilibrium Values 1.4: Dynamic Economic Applications 1.5: Applications of Dynamics Using Spreadsheets 2: First Order Dynamical Systems 2.1: Solutions to Linear Dynamical Systems with Applications 2.2: Solutions to an Affine Dynamical System 2.3: An Introduction to Genetics 2.4: Solutions to Affine Dynamical Systems with Applications 2.5: Application to Finance 3: Introduction to Probability 3.1: The Multiplication and Addition Principles 3.2: Introduction to Probability 3.3: Multistage Tasks 3.4: An Introduction to Markov Chains 4: Nonhomogeneous Dynamical Systems 4.1: Exponential Terms 4.2: Exponential Terms, a Special Case 4.3: Fractal Geometry 4.4: Polynomial Terms 4.5: Polynomial Terms, a Special Case 5: Higher Order Linear Dynamical Systems 5.1: An Introduction to Second Order Linear Equations 5.2: Multiple Roots 5.3: The Gambler's Ruin 5.4: Sex-Linked Genes 5.5: Stability for Second Order Affine Equations 5.6: Modeling a Vibrating String 5.7: Second Order Nonhomogeneous Equations 5.8: Gambler's Ruin Revisited 5.9: A Model of a National Economy 5.10: Dynamical Systems with Order Greater than Two 5.11: Solutions Involving Trigonometric Functions 6: Introduction to Nonlinear Dynamical Systems 6.1: A Model of Population Growth 6.2: Using Linearization to Study Stability 6.3: Harvesting Strategies 6.4: More Linearization 7: Vectors and Matrices 7.1: Introduction to Vectors and Matrices 7.2: Rules of Linear Algebra 7.3: Gauss-Jordan Elimination 7.4: Determinants 7.5: Inverse Matrices 8: Dynamical Systems of Several Equations 8.1: introduction to Dynamical Systems of Several Equations 8.2: Characteristic Values 8.3: First Order Dynamical Systems of Several Equations 8.4: Regular Markov Chains 8.5: Absorbing Markov Chains 8.6: Applications of Absorbing Markov Chains 8.7: Long Term Behavior of Solutions 8.8: The Heat Equation

ISBN: 9780195084382
ISBN-10: 0195084381
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 444
Published: 1st June 1993
Publisher: Oxford University Press Inc
Country of Publication: US
Dimensions (cm): 24.3 x 16.2  x 3.4
Weight (kg): 0.77