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Full Description
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.
Contents
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
