Differential equations for engineers does justice to its name. This is a book intended for those interested in differential equations and their real world applications. Since the book is targeted towards engineers and not math majors, it is worth mentioning that the author does a nice job of presenting the bare minimum details of the proofs for almost every topic discussed in the book without presenting all the gory details.
It begins with good motivation: several appealing applications of differential equations that cover a variety of disciplines ranging from electrical to civil engineering. Other applications are discussed in subsequent chapters as well. In particular, I find solving problems such as water purification in a stream using differential equations quite interesting. In a certain sense, this could stimulate the minds of readers and introduce them to solving problems motivated by phenomena in biology using the approach of mathematical modeling. The water purification problem can be considered as analogous to problems associated with purification of blood in certain disease states.
Some of the chapters contain identical example problems. For instance, the examples used to discuss the Laplace transform in Chapter 6 complement those in chapter 5 and could help the reader identify different methods used by linear differential equation solvers. One of the major highlights of this book is Chapter 10, where extremely clear schematics illustrate the different numerical methods of Euler, Runge Kutta (RK), etc. The figure illustrating the RK method is one of the best I have ever encountered in any book on numerical analysis for undergraduates. The final chapter, on solving differential equations with Maple, is useful and should help the reader become aware of differential equation solver packages. The summary section at the end of every chapter serves to provide a nice overview about all the topics discussed.
This is an interesting book, with well explained concepts and good examples in every chapter, some of which are rarely found in textbooks of differential equations. Some of the chapters on applications could raise important questions and lead to interesting thoughts on how mathematical modeling can help solve real-world problems. This may not be the right book for Math majors to learn about differential equations, because most of the proofs are not rigorous and are at times oversimplified. On the other hand, since the book targets engineering students, it is understandable and full of nice examples.
Lakshmi Chandrasekaran (firstname.lastname@example.org) is a postdoctoral fellow at the Louisiana State University Health Sciences Center. She works in Mathematical and Computational Neuroscience. Whenever she has some free time she like to read pretty much anything and to listen to music.
1. Introduction; 2. First-order and simple higher-order differential equations; 3. Applications of first-order and simple higher-order equations; 4. Linear differential equations; 5. Applications of linear differential equations; 6. The Laplace transform and its applications; 7. Systems of linear differential equations; 8. Applications of systems of linear differential equations; 9. Series solutions of differential equations; 10. Numerical solutions of differential equations; 11. Partial differential equations; 12. Solving ordinary differential equations using Maple; Appendix A. Tables of mathematical formulas.