****** - Verified Buyer
4.5
I used this text to teach differential equations to advanced high school seniors and it worked extremely well. After considering several other texts, I was sold on this book for three reasons:1. Rather than older-style differential equations books that focus on analytic methods, this book has a consistent approach of using a combination of analytic, qualitative, and numerical methods. As an industrial mathematician, most differential equations that I worked with could not be solved analytically and thus numerical and qualitative techniques became key tools.2. The friendly expository style of the authors motivates the material and is easier for students to understand than more formal textbooks. New material is always introduced by concrete examples before getting into theory.3. The book is written from a dynamical systems point of view and the authors tap into many interesting results from the past 40-50 years, e.g., the Lorenz equations, modeling epidemics, adaptive shock absorbers, etc.Perhaps my most pleasant surprise teaching the course was how much the students liked and learned from DETools, the differential equation software that comes with the textbook. We regularly used DETools in class (there's essentially no learning curve) and its use energized the students and made much more clear to them the nature of solutions.I also found the exploratory projects at the end of each chapter very valuable. My students liked the challenge of these more general and open-ended problems, and the projects solidified their understanding.As far as the nuts and bolts of teaching the course, I typically covered one section per day, and we did most of the sections in Chapters 1-6. Regrettably we didn't get to the last two chapters of the book, but they are quite good. Chapter 7 gets into the nitty gritty of numerical methods (e.g., effects of finite arithmetic) and Chapter 8 is a nice introduction to discrete dynamical methods. (A one-semester course in differential equations can only cover so much, so the text leaves to a later course many special techniques for analytically solving ODEs and it does not cover boundary value problems or the Fourier method.)In summary, I am in very much in agreement with August 7, 2013 review by "G Cantor" that "it would be difficult to find a better introductory text for ordinary differential equations." This text is a great intro that makes the subject come alive and does an excellent job preparing students to work with differential equations both in later college colleges and in the real world.
