Topics in Mathematical Modeling by Difference Equations by Garvey, Paul R.;

Short description:

This book seeks to illuminate this powerful framework by integrating theoretical insights with practical applications. It serves to provide a clear introduction to the calculus of finite differences and first-order difference equations and to guide readers toward advanced methods for deeper exploration. 

Long description:

"This is the best introductory book that I have seen to help one learn about and understand the mathematics and applications of difference equations. I wish it was available when I was a student."

—Professor Ronald E. Mickens

“This book shows a wonderful synergism between difference equations and mathematical modeling.”

—Professor Nancy Rallis

Across the vast array of topics in applied mathematics, difference equations stand out as essential tools for analyzing and understanding discrete systems and processes. Their applications span diverse fields: from modeling biological population dynamics to economic systems, numerical approximations of differential equations, and even supply chain optimization. The versatility of difference equations underscores their relevance in tackling a wide range of disciplines and real-world challenges.

Mathematical Modeling by Difference Equation with Mathematica seeks to illuminate this powerful framework by integrating theoretical insights with practical applications. It serves two primary goals: to provide a clear introduction to the calculus of finite differences and first-order difference equations, and to guide readers toward advanced methods for deeper exploration. This text is written for undergraduate students in mathematics, business, economics, and other quantitative sciences.

Researchers and professionals who use mathematical modeling in their work, and anyone intrigued by the role of mathematics in understanding discrete systems, will also find tremendous value in this text.

Features

• Numerous exercises and worked examples with solutions provided


• Appendix including samples of the Mathematica code used in the book


• Extensive real-world applications with examples from fields as diverse as physics, biology, and economics.

"This is the best introductory book that I have seen to help one learn about and understand the mathematics and applications of difference equations. I wish it was available when I was a student."

—Professor Ronald E. Mickens

“This book shows a wonderful synergism between difference equations and mathematical modeling.”

—Professor Nancy Rallis

Table of Contents:

1. Elements of the Difference Calculus  1.1 Introduction  1.2 Finite Difference Operators and Operations  1.3 A Bouncing Ball Model  2. First-Order Difference Equations  2.1 Introduction  2.2 Autonomous and Nonautonomous Linear Difference Equations  2.3 A Tour of First-Order Nonlinear Difference Equations  2.4 Linear Systems of Difference Equations  2.5 A Supply Chain Linear System  3. Difference Equation Models  3.1 Loan Amortization Model  3.2 Modeling Differential Equations by Finite Differences  3.3 LaborManagement Negotiation Model  3.4 RuralUrban Migration Model  3.5 Discrete-Time Markov Models  3.5.1 Gambler’s Ruin  3.5.2 Disease Transmission  3.5.3 Product Manufacturing and Distribution  4. Behavior of Difference Equation Models  4.1 Sequences, Fixed Points, and Model Behavior 4.2 Periodic Points, Cycles, and Stability  4.3 Ricker Model of Population Dynamics  4.4 Higher-Dimensional Discrete Models  4.4.1 Nicholson-Bailey Host-Parasitoid Model  4.4.2 Elementary Epidemic Models