I had to use this book as a text for a class on Matrix Theory. It is really hard to learn much about matrices from this book. It is poorly organized and assumes you already know a lot. Two quarters of graduate level linear algebra was not enough. I actually drew on results from a number of different graduate courses (diffential equations, real analysis, etc.) to help me and still found this book difficult to learn from.

Many of the sections of the book present key material in a very general way. The proofs are often very condensed and sometimes use more advanced results that can only be found with outside research. Many of the problems are very difficult and require advanced techniques not presented in the book.

Two positives - it has an extensive bibliography and could be a good source of challenging problems for the more advanced student.

I have been using this book for many years as a reference and as a source of interesting diversions. Bellman's typically dense style and leaving some proofs to the reader makes for a lot more material than its 387 pages would indicate. The main topics begin with matrix theory in maxima and minima and quickly get to dynamic programming, differential equations, and stability theory. This is the one good reference I have found on Markov matrices (not Markov processes). The last few topics are control processes, invariant imbedding, and Tychonov regularization. Side topics include Vandermonde matrices, Gaussian quadrature, and much, much more.

I found this book too steep for my abilities. I was attracted to its small size, for I hoped that this would provide an easy way to understand DE's. However, I should have remembered what Pythagoras told the anxious king: "There is no royal road in mathematics." This book is a case in point. The reason for its brevity are that its demonstrations are terse, and it provides only occasional answers to the problem sets. Moreover, I find it asumes that the reader is an astute mathematician.
The book might serve as a good refresher (see other review comments), but not a sufficient introductory text for someone with no previous experience in DE's or at the very least, someone who does not have a strong mathematics background. I gave this book 2 stars and not 1, only because part of the problem might be me. I believe I will do much better with Schaum's book on differential equations in their Outline series--a much bigger book, of course.

I bought this book to review my differential equations, which I had taken years ago and had mostly forgoten. I foudn it useless: it seems to cover all the essential aspect of D.E. that would belong in a introductory text, and to have reasonable rigor. However, it went to fast, was not well organized, and was generally hard to follow. I found that I was lost within a few pages, dispite having successfully completed classes on the material in the past. I've seen more advanced texts on things such as advanced calculous and partial D.E.s that were easier to understand than this. Anyway, I don't have another book to suggest, but I would avoid this one.

I bought this book as an aid to a differential equations course I had as an undergrad, and I found that it was lacking in sufficient examples. The text itself was easy to follow and logical, but the derivations of the equations and finding the solutions to the diff eq's were rather brief with few intermediate steps. It does, however, explain the applications of the mathematics to other fields such as physics, engineering, even biology. It even includes a few computational computer programs to illustrate the applications in computer science. It was an ok book to read, but was weak in the area of "teaching from the blackboard."