This text is THE single best book on mathematics that I have ever read. Goodwine's genuine care for his students and desire to spread knowledge of Diffeq was poured into this book to create a beautiful and simple method of learning. As one of Goodwine's students, his class was rigorous, but this text made it manageable. This is the type of book that you could learn the entire subject with on your own. It is full of relevant engineering examples applicable to practical applications that are clearly explained with relevant figures. I relied heavily on this book to teach myself Diffeq II when Goodwine was not my professor, with great success. I cannot recommend it highly enough and I'm very grateful to have found this book.

Coming from someone who has had to sit through 4 semesters of college math classes in the areas of calculus and linear algebra, this book is refreshing. It gives you a way of seeing what you have worked toward - real life application of math. It is loaded with examples, a descriptive and easy to follow table of contents, the right amount of problems at the end of each chapter, and best of all: zombie references. This book was used in my two vibrations and controls classes and I've read it every step of the way (and no I'm not the student who always does their reading but I know for a fact that for this book - it DOES work).Do note: The man who wrote this book teaches my class BUT he has never asked us to review his book. I write this review simply because not only do I think the book is great I also think Dr. Goodwine is the type of guy you want writing your Differential Equations Book: a man genuinely interested in the well-being and intellectual advancement of each of his students. This sort of philosophy will lead one to write a book and write it well.

This book is definitely not of the norm when it comes to higher level books in mathematics. Most give the equations, give the derivations, then expect the reader to apply that pure math into life. Not so with Dr. Goodwine's book. I have learned more about applying mathematics to real-life situations in the two semesters that I have used this book than I have in any other book that I have been presented with. I strongly recommend this book to whoever may be seeking a great book discussing the usefulness of Differential Equations and the theory behind these applications. It may be nerdy of me to say, but it has been truly enjoyable learning from this book! Thanks!

This is the most helpful math book I have ever had. It's very readable and has many examples that seem to make the stuff worthwhile. It links differential equations to real world problems, including vibration and control theory. It even includes a problem about the zombie apocalypse. This book would be very helpful for someone with a professor who expects you to teach yourself. If I don't understand in class, or if I miss a class, I can usually read the book and pick it up. This is a very well written, comprehensive overview of differential equations.

In the interest of full disclosure, I graduated from the University of Notre Dame with a BS in Mechanical Engineering having taken 3 semester classes from Professor Goodwine, 2 of them explicity requiring this book. That said, as a professor Goodwine knows quite well what does and does not hold his students attention in a class room. Knowing how to help his students learn (or teach as some might say) translates well into this book. Any one who has ever had to teach themselves out of the book for lack of a gifted professor knows that not all books are created well for this purpose. Should you find your class to be you and this book you will find all the tools you need. There are numerous examples given per chapter, and per topic to help further develop your understanding of the theories and equations that are presented to you.I kept most of my books from college, but this is one of the ones I continue to reference and use. If you wish to remember or learn about differential equations and their applications, this is the book for you.