Introduction to Differential and Difference Equations through Modeling

1. Auflage 2025
ISBN: 978-1-032-94900-0
Verlag: Taylor & Francis Ltd

Buch, Englisch, 355 Seiten, Format (B × H): 174 mm x 246 mm

Reihe: Textbooks in Mathematics

This book presents an opportunity to learn difference and differential equations through a modeling-first approach. The text is meant as an introduction to those equations and not as a text only for modeling courses. No previous exposure to these equations is expected. Modeling in Introduction to Differential and Difference Equations through Modeling is presented as the vehicle for learning difference and differential equations.

Although the topics in difference and differential equations are consistent with those in other textbooks, this approach differs. The presentation starts with a model (or several models) and offers the solution with minor discussions. Then, methods to obtain those solutions are presented and show these same models and others again in more detail.

This approach is designed to focus on the use of difference and differential equations to solve real-world problems, and to learn not only these primary topics, but how to apply these through modeling.

The authors begin with a review of matrix algebra, then an introduction to modeling. The text progresses to discrete dynamical systems, and then to the standard organization of most differential equation texts, making the alignment with a current syllabus easier.

Technology is a significant modeling component. Excel®, Python®, and Maple® are presented as methods to solving the models. This material has been class tested at the US Military Academy at West Point, Marian University, the College of William & Mary, and the Naval Postgraduate School with great success.

Zielgruppe

Undergraduate Core

Autoren/Hrsg.

Burks, Jr.

Fox, William P.

Burks Jr., Robert E.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1. Matrix Algebra Review

2. Mathematical Modeling and Technology for Difference and Differential Equations

3. Modeling Discrete Dynamical Systems (DDS)

4. Systems of First Order Difference Equations

5. Introduction, Basic Concepts, and Techniques in Modeling First Order Ordinary Differential Equations

6. Modeling with Numerical Solutions to Differential Equations---IVP for ODEs with Technology

7. Numerical Output for Analysis: Graphical and Percent Error

8. Higher Order Differential Equations

9. Higher Order Numerical Methods to Solve IVP and BVP

10. System of Linear and Nonlinear ODEs

11. Numerical Solutions to Systems of ODES

12. Modeling using Laplace Transforms

13. Answers to Selected Exercises

Über Autor(innen)

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 Press

Modeling Change and Uncertainty Machine Learning and Other Techniques, 2022, CRC Press

Mathematical 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.