Differential Equations and Their Applications: An Introduction to Applied Mathematics

I like this book for its excellent examples of applications.Later chapters give intro to linear algebra and Laplace transforms and delta function in an easy manner.I learnt these advanced topics from this book.This is not an ordinary class text book, but a good supplementary one....needs wider advertising.

This book is extraordinarily clear as well as being concise (but never too much so) in the mathematical parts. Discussion of applications is verbose, but is kept in separate sections; this material can be omitted entirely or read later without any detrimental effect to the flow of the book. However, the discussion of the applications is interesting and deep, and would be useful (and fun) for motivated students to read. The book begins with a no-nonsense discussion of how to solve differential equations analytically. Unlike many books, it gives clear instructions to the reader as to how to know which techniques are applicable. Also, it does not introduce qualitative or numerical methods until it has already developed a number of analytic techniques, and in my opinion, this results in greater clarity than the path most books take of integrating (or should I say jumbling?) the material together. The book gradually and logically covers the ground between analytic and numerical, moving towards actually writing algorithms, which are included in the text. The emphasis is always on understanding. Exercises are straightforward and useful. My only complaint is that, in this modern age, the C programs should be included in the text and the Pascal and FORTRAN ones relegated to the index. (It is the other way around, alas.) This book is simply wonderful for anyone studying differential equations for the first time. I do not understand why undergraduate institutions use the more commercialized texts instead of ones like this. This is a great book; it would be excellent for a textbook or for self-study.

As an academic I rarely if ever use textbooks because I find their writing style bland and disengaging--especially in my own area (economics). Braun's text is the exception to the rule: this is a textbook that is so well written it could qualify as entertainment. At the same time the major issues in the field are covered well, complete with an overview of the linear algebra required for doing ODEs and a good introduction to nonlinearity and chaos. It may not, as one reviewer notes, provide a complete and rigorous coverage of this highly technical field, but it does what a text should do but so few achieve: it excites its readers and inspires them to delve further into this fascinating discipline.

I have used this to teach DE's in a one to one tutoring context for a couple of years now, since I first picked it off a library shelf and felt literally like jumping for joy over how good it was. Not that I dislike Boyce / DiPrima, but suddenly I had a text that was really fun! Now, this is definitely a "what DE's are good for" kind of text, so if you feel that your students should suffer teething pains on a dry theoretical tome, this is NOT the book for you. Nevertheless, having had students chew up all their available time on this book, because they loved it, makes me recommend it highly.

This book covers its material thoroughly and clearly with the most interesting set of applications I've seen in a high-level text. It also contains all the linear algebra needed to understand the material. This book was based on a course the author taught. Indeed, Braun's claim that students taking linear algebra would refer to his course for a refresher is well-deserved. Exercises are generally difficult but the examples are easy to follow. Buy this if you want to truly understand the subject matter.