Topics in Mathematical Modeling by Difference Equations

With Mathematica
1. Auflage 2026
ISBN: 978-1-041-12203-6
Verlag: Taylor & Francis Ltd

Buch, Englisch, 568 Seiten, Format (B × H): 178 mm x 254 mm

"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.

Zielgruppe

Undergraduate Advanced

Autoren/Hrsg.

Garvey, Paul R.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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

Über Autor(innen)

Paul R. Garvey, Ph.D., is a Distinguished Chief Scientist at The MITRE Corporation, a not-for-profit organization that operates federally funded research and development centers in support of the U.S. government. He is the author of more than 30 peer-reviewed publications and four textbooks published by Chapman & Hall/CRC Press.

His academic and teaching experience spans both mathematics and systems engineering. At Boston College, he designed and taught the upper-level mathematics major elective Mathematical Modeling for many years. He also served as an adjunct associate professor in the Department of Engineering Management and Systems Engineering at Old Dominion University, where he taught the graduate course Engineering Systems Risk Analysis.