Introduction to Differential and Difference Equations through Modeling

Dr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles.Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor in the Defense Analysis Department of the Naval Postgraduate School (NPS) and the Director of the NPS’ Wargaming Center. He holds a Ph.D. in Operations Research from the Air Force Institute of Technology. He is a retired logistics Army Colonel with more than thirty years of military experience in leadership, advanced analytics, decision modeling, and logistics operations who served as an Army Operations Research analyst at the Naval Postgraduate School, TRADOC Analysis Center, United States Military Academy, and the United States Army Recruiting Command.Other book by William P. Fox and Robert E. Burks: Advanced Mathematical Modeling with Technology, 2021, CRC Press.Other books by William P. Fox from CRC Press:Decision Analysis through Modeling and Game Theory, 2024, CRC PressModeling Change and Uncertainty Machine Learning and Other Techniques, 2022, CRC PressMathematical Modeling in the Age of the Pandemic, 2021, CRC Press.Advanced Problem Solving Using Maple: Applied Mathematics, Operations Research, Business Analytics, and Decision Analysis (w/William Bauldry), 2020, CRC Press.Mathematical Modeling with Excel (w/Brian Albright), 2020, CRC Press.Nonlinear Optimization: Models and Applications, 2020, CRC Press.Advanced Problem Solving with Maple: A First Course (w/William Bauldry), 2019. CRC Press.Mathematical Modeling for Business Analytics, 2018, CRC Press.

• 1. Matrix Algebra Review2. Mathematical Modeling and Technology for Difference and Differential Equations3. Modeling Discrete Dynamical Systems (DDS)4. Systems of First Order Difference Equations5. Introduction, Basic Concepts, and Techniques in Modeling First Order Ordinary Differential Equations6. Modeling with Numerical Solutions to Differential Equations---IVP for ODEs with Technology7. Numerical Output for Analysis: Graphical and Percent Error8. Higher Order Differential Equations9. Higher Order Numerical Methods to Solve IVP and BVP10. System of Linear and Nonlinear ODEs11. Numerical Solutions to Systems of ODES12. Modeling using Laplace Transforms13. Answers to Selected Exercises