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Rating: 
Summary: Learning D.E.'s Can Actually be Fun
Review: 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.
Rating:
Summary: One of the best in the field
Review: This book covers its material thoroughly and clearly withthe most interesting set of applications I've seen in ahigh-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.
Rating: 
Summary: Nice try, but...
Review: This is the typical mathematics book intended for non-mathematicians. The author made a great effort to compile the most diverse examples of problems (better said MODELS of problems) that can be solved employing mostly ODE and some PDE techniques. However, I think this kind of books fail to show what mathematics is, and how mathematics should be used to solve problems coming from other fields of knowledge.First, the book does not cover thoroughly the theory for the linear case, which could be carried out without any effort up to the n-th order. Second, it does not tell explicitly the great difference between the linear and the non-linear cases. Third, eventhough it includes some material on systems of differential equations, it doesn't exploit the fact that a n-th order equation can be viewed as a n-th order system of of 1st order equations. Fourth, everything is mixed up: in the same chapter you find elementary concepts of linear algebra (that the student should be supposed to master), some miscelaneous applications, and, if you are lucky, some theory on differential equations. Fifth, it gives a wrong idea of the meaning of solving an ACTUAL problem. The fact that we are able to give a nice solution to a highly simplified model we have built does not mean that we have found a practical solution to the problem we actually face up in the real world, and moreover it does not mean that we will always succeed to give a useful answer by employing these tools. When you try to solve a problem that you don't know thoroughly you take the risk of building castles in the air. I think that if you are interested in applying mathematics you should start first by learning all the necessary theory and then study carefully the problem you are interested in. And don't forget the most important of all: the theoretical solution to an actual problem must be confirmed by experimentation, something this book does not point out. To tell something positive about it let me say that you will find a lot of challenging excercises, some of its "application" problems are interesting, and if you are a teacher it will serve well as a companion text for real treatises on differential equations like Coddington's or Kaplan's. Please check my other reviews at my member page (just click on my name above).
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