ISBN0155209841

I had to buy it for an engineering math course. It is truly aweful. It has proof after proof and theorem after theorem with very few examples. Very abstract explanations. I do not know if anyone could learn anything from this book except to buy a different book if you really want to learn linear algebra. I just purchased a different Linear algebra book so I can understand the material. Take the advice of someone who has used the text and do your self a favor. Do not buy this book not even as a joke.

I used this for a introductory differential equations course. All the reviewers are dead on. This book will make you hate math with a passion such as you have never known.

I think the other reviewers all looked at this book from the perspective of an engineering major who wasn't interested in learning the topics but just wanted to get through a required course without having to put in the effort to understand the material. This book does an excellent job of tying together the two topics at hand. Yes, like any good math book, there are lots of proofs. Of course, I'm reading this from the perspective of a graduate student in geochemistry with a bachelors degree in math from several years ago. It's a great reference/review book for me. So, I'd just like to counter the other reviewers by saying if you're looking for a book with a good concise theory based introduction to Differential Equations and Linear Algebra, this is the best one I've seen.
One final note -- I think this web form is screwy, I can't correct the repeated sentence above...

This book doesn't explain s***! It's the worse math book out there. To many theorems and not to many problems. Look for another ODE & Linear Algebra book if you can.

This book is excellent. I'm shocked at the low ratings, BUT I think I can explain why. This is one of the best introductory books out there. I used it in my first class as an engineering student before I switched over to a mathematics major. Classes for math majors don't normally use this book because it is too elementary. But for non-math majors (engineering, chemistry, physics, ...) this is the first book of choice. Unfortunately, these majors are also full of people in the early years who won't like differential equations. Therefore, this book gets a lot of negative attention from disenchanted students. I love differential equations, but many people who see themselves as good in math get an unexpected bad grade in this class--they can't accept that and instead fault the book or the teacher. I admit, differential equations seemed to me at first to have too much clever guessing, no single structured methodology with which to apply to every differential equation, and most annoying is that most differential equations can't be solved in closed form anyway. This situation is not the fault of the book. Even today there are folks getting PhD's by working on unsolved differential equations.

For those who want more help, I believe in having lots of practice problems. So, in addition to this book, get the "Schaum's Outline of Differential Equations" by Bronson (ISBN: 0070080194) for slightly more than $10 (cheap). Also, I believe in reading more than one source simultaneously, so get "Ordinary Differential Equations" by Tenenbaum and Pollard (ISBN: 0486649407) (Also cheap), and read it along with Rabenstein's book. Tenenbaum's book might be just as good or better as Rabenstein's book, so it might be wise for the instructor to use Tenenbaum's book instead of Rabenstein's book and help the student save some money. But I suspect Rabenstein's book is still more elementary in treatment.