Ordinary Differential Equations [Paperback]

The book consists of six major subtopics: first-order equations, general nth-order linear equations, systems and nonlinear equations, series solution methods, numerical solution methods and existence/uniqueness theorems. Most of the subjects tend to be divided into two or three chapters, with the first one or two containing the theoretical aspect and computational techniques and the other consisting of applications to real world problems.

At some 800-odd pages the book is quite long, but the sheer amount of material covered is simply astounding; the book has several types of special ODEs and solution methods that I have not seen anywhere else, and the authors go to great lengths to make every concept fully clear to the reader while still being quite rigorous. I am personally somewhat pure-math oriented but also needed some practice with applied problems, and this text is sure to please both students of mathematics as well as those of the sciences due to the very large amounts of subject material contained in both areas. (the book is split about 55-45 in theory/application)

One very nice thing is that if there is some doubt as to whether or not the reader is comfortable with something from another subject (i.e. real analysis), the book does not assume that the reader is familiar wih that topic, but rather it goes through a short review of the topic that is self-contained enough for readers who have not heard of the topic before to get a good idea of it. There are a variety of well-designed problems that provide plenty of practice along with some that expand upon the original concepts, and the average difficulty generally seems about right for the target audience. The numerical methods are also surprisingly robust considering that the book was written in 1963 and calculators/computers were not all that standard. Also, as was remarked earlier, this is one of the very few texts out there that contains the answers to all of the exercises, making it perfect for the self-study that I used it for; other authors/publishers should learn from this.

All things considered, this ranks among the best textbooks on any subject that I have ever seen, and coupled with the extremely low price, it definitely lies in the "must buy" category.

No Hardcover, No Solutions Manual, Format is bland, hard to write your own notes, and the physical quality is weak. More suited for a tom clancy novel than a Textbook.

All in all though if this were your only book in ODE...you would learn ODE well. Answers to most problems and good examples. Easy to follow. I think most of the problems areas are cause by the publisher trying to save money and lower the retail price than the author's ability to produce a quality text book. I hope the authors get picked up by Wiley or Adison-Wesley not a weak discount publisher like Dover.