Modelling with Ordinary Differential Equations

This is a textbook for an advanced undergraduate or early graduate-level course in ordinary differential equations.  The first half of the book contains a fairly standard collection of material on ODE's including some elementary solutions methods, existence and uniqueness theorems, the stability of equilibrium solutions, Lyapunov functions, and Sturm-Liouville problems.  The second half of the book contains brief introductory chapters on numerical methods for ODE's, the calculus of variations, optimal control, inverse problems, differential games, stochastic differential equations, and neural networks for ODE problems.

 

As important as what is included in this book is what is excluded.  Although modeling is prominent in the title, and many well-known ODE models are presented as examples in the book, there is very little discussion of the modeling process or how ODE models could be applied in practice.  Unlike many other recent textbooks in this area, there is little or no discussion of the theory of dynamical systems and chaos.  For a textbook, it is surprising to find that there are no exercises.

 

This book may be of interest to instructors who are interested in teaching ordinary differential equations without dynamical systems and want to include some of the special topics in the second half of the book.  

Brian Borchers is a professor of mathematics at New Mexico Tech and the editor of MAA Reviews.