Customer Reviews

Differential Equations and Dynamical Systems

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Perko's book is one of the best books that gives an advanced introduction to dynamical systems from the point of differential equations. Many other good books tread the same ground, without emphasizing the connection to ODEs. Perko's text is particularly strong in several respects. First, the dynamical systems it considers are almost always expressed in terms of underlying differential equations. Second, it gives proofs or outlines of proofs of most major theorems used in this field. Third, it covers the most important topics, including: local theory of hyperbolic equilibria, invariant manifolds, Hamiltonian systems, flows on R^2, stability theory, and elementary bifurcations. Also reviewed are the results from linear systems theory, in a particularly well-written and easy to follow introductory chapter. Another great feature of this book is its solid coverage of center manifold theory, which is an important and somewhat difficult topic.

There are a couple of problems with this book. The proofs to some of the major theorems are occasionally abstruse or poorly derived. Perko seems to bend over backwards to give analytical proofs, when algebraic or topological proofs might be easier. Many of the problems reuse the same elementary example equations. This is OK insofar as it allows the reader to see how different techniques can be used to analyze the same systems, but it limits the reader's exposure to the full variety of interesting dynamical systems that can arise in practice. The author also tends to emphasize polynomial vector fields, which is a potential limitation. Occasionally the problems are significantly more difficult than the examples worked in the text.

Overall, Perko's text is a very solid introduction to advanced ODEs and continuous dynamics. It is especially well-suited for scientists and engineers who want a readable introduction to the qualitative theory of ODEs.

This book is a useful textbook for advanced courses on differential equations and dynamical systems for senior undergraduate students or first year graduate students.

The book presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.

The book has a sketch of the proof of the Hartman-Grobman Theorem which was useful for my second undergraduate course on dynamical systems and nonlinear differential equations.

I liked the book and I am quite sure it will become a classic textbook on this very useful branch of Math that has so many old and new applications in Physics, Economics and Finance.

I used this book the last two times I taught ordinary differential equations at the graduate level. It's a decent book and it covers a lot of topics, but it has an amazing amount of errors, given that it is already in its 3rd edition. Some proof techniques I find archaic (for example, the insistence on Picard iterations, where a single call to Banach's fixed point theorem would be much clearer). A good point are the many exercises, but again, they can contain typos.

The kindle is a fine piece of technology and I have heard from my colleagues that most textbooks translate well into that format, but something went wrong in the conversion of this textbook. I do not know what it is, and it may even be fixed by the time you read this, but the version that I have on my kindle will occasionally scatter the math text around the page. I think this is something that can be fixed eventually. Most of the text renders the way it is supposed to. And most of the time if the text does something weird I can figure out what it is supposed to say. However, there are a few times when it is just too badly scattered to figure out. The problem appears on both my Kindle and on my computer with KindlePC, so I am sure the problem is with the book itself.

So far the worst instance of the book not rendering correctly is problem 5 at the end of section 1.9. I was forced to borrow my instructor's book to finish the homework assignment.

As far as the text itself, I cannot say much good or bad about it. Differential Equations is not my favorite subject, and the text is just kind of boring. I do not know if that is completely my own bias or if the textbook is poor or something in between, but I was not impressed.

But if you must get this book, do not get it in electronic form.

This book was required for my class. It is a good book if you know the topic and want to use it as a reference. Very strong material, but I feel like I could have learned the material better from a friendlier book.

But that is opinion based, maybe you'll have better luck (I might just be stupid?).