1st Edition
Topics in Mathematical Modeling by Difference Equations With Mathematica
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
Biography
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.
"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
