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Differential Equations and Dynamical Systems (Anglais) Relié – 1 février 2008

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Book by Perko Lawrence

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28 internautes sur 29 ont trouvé ce commentaire utile 
Very good graduate ODEs text, with some flaws 12 décembre 2003
Par David Elder - Publié sur Amazon.com
Format: Relié
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.
7 internautes sur 7 ont trouvé ce commentaire utile 
Very incomplete and uninsightful 11 avril 2012
Par Steven Skees - Publié sur Amazon.com
Format: Relié Achat vérifié
This text was the assigned text for the first semester of a graduate level mathematical modeling course which I had taken, and it was an incredibly painful book to work with. One complaint which I often heard from classmates was the lack of examples in this text. Normally, I'd think that such a complaint is somewhat invalid for such an advanced level text, as students should be focusing more on theory than on specific problems at this stage... but the problem here is that the material contained within the text is incredibly weak on the theory and zeroes in on the same boring and uninspiring exercises... which are repeated with a "new hat" in so many sections. Theorems are stated in a manner which many people (including my own professor, whom actively conducts research in this area) found to be incredibly confusing, and a lot of the proofs read like some of the worst hand-waving ever, with never-ending references to other sources for proofs. Rudin's Principles of Mathematical Analysis is a popular one which he often refers to, but many times, Perko will skip a detail on a proof and refer to some text which cannot be found in even some of the greatest university libraries. To me, it seems ridiculous that a student should go on a wild goose chase to piece together proofs from essentially unavailable sources, when they can actually often be done in a much simpler manner.

Unfortunately, even the publisher, Springer (which is typically known for only the highest quality products), has truly dropped the ball on this book, by allowing it to be published with typos scattered EVERYWHERE... including typos which drastically affect the entire meaning of a theorem. Worse is that they have done several reprints of this precise edition of the text, and the typos which were elemented in one reprint may reoccur in the next reprint. There was even one occasion where my professor had to provide me with an opportunity to redo an entire assignment, because he was incredibly confused by my results. As it turned out, upon going to his office for assistance in the corrections, he noticed that my text had multiple critical typos in a theorem which was to be applied to each exercise, and he had to allow me to borrow his text to copy down the correct information.

My main gripe with this book is the exercises. Essentially, there is absolutely NO ingenuity or creativity on the exercises, and you essentially end up doing the same small handful of exercises over and over again, just piling on new techniques which are covered in the new section. I don't know if repeating exercises over and over again was a deliberate effort to make students feel comfortable with the material as it was repeated, or if it was just sheer laziness. But in any event, it really wasn't helpful, and made depending solely upon very basic concepts (often ones learned in prerequisite courses) rather than what this text should be covering very tempting. The worst part is that the exercises presented in the text, as boring and uninspiring as they are, include a ton of elementary busy work, very labor-intensive and time-consuming, to produce very meaningless results.

In all fairness, this is an area of mathematics which is relatively new, and it seems that there haven't quite been any solid "standards" which have arisen in this area yet. But in the meantime, there certainly are some better texts. There are several textbooks out there which cover this material, but each one is very unique in the manner in which it presents the material, the "essential" material needed, and the level of rigor used within. Hopefully any "standard" text which does arise is in no way inspired by this text.
1 internautes sur 1 ont trouvé ce commentaire utile 
a solid introduction to dynamical systems 7 mai 2012
Par C - Publié sur Amazon.com
Format: Relié Achat vérifié
I took an upper-level undergraduate / graduate class in ODEs and dynamical systems a year ago and it used this textbook. Perko is decent introduction to dynamical systems, but it is best used with a few supplementary texts (specifically, Smale, Hirsch and Devaney's Differential Equations, Dynamical Systems, and an Introduction to Chaos, and V.I. Arnol'd's Ordinary Differential Equations). I agree with the reviewer who calls it "a very good graduate ODEs textbook with some flaws" -- that's generally how I felt about it, too.
13 internautes sur 19 ont trouvé ce commentaire utile 
A Book on Advanced Dynamical Systems 7 avril 2000
Par Juan P Medina-Mora - Publié sur Amazon.com
Format: Relié
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.
1 internautes sur 1 ont trouvé ce commentaire utile 
Review Lawrence Perko purchasing 19 février 2013
Par Julian Murrieta Valladares - Publié sur Amazon.com
Format: Relié
A big reference on differential equations field, Lawrence Perko's text is full of exercises, almost all theoremes have thier proofs, and in general goes deep into the subjet: linear and non linear differential equations systems. Delivering was great and fast! Excellent purchase on Amazon!
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