Buy Differential Equations and Dynamical Systems (Texts in Applied Mathematics) on ✓ FREE SHIPPING on by Lawrence Perko ( Author). Differential Equations and Dynamical Systems by Lawrence Perko, , available at Book Depository with free delivery worldwide. Differential equations and dynamical systems / Lawrence Perkord. ed. p. cm. – (Texts in applied mathematics ; 7). Includes bibliographical references and.
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This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem.
In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations. The text succeeds admiraby Examples abound, figures are used to advantage, and a reasonable balance is maintained between what is proved in detail and what is asserted with supporting references Each section closes with a set of problems, many of which are quite interesting and round out the text material All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.
In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise’s algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.
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Page 1 of 1 Start over Page 1 of 1. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Edition Studies in Nonlinearity Volume 1. Introduction to Real Analysis. Review Reviews from the first edition: Texts in Applied Mathematics Book 7 Hardcover: Springer; 3rd edition April 1, Language: Try the Kindle edition and experience these great reading features: Share your thoughts with other customers.
Write a customer review. Read reviews that mention differential equations dynamical systems equations and dynamical graduate level proofs theory exercises textbook theorem advanced proof solid theorems class course covers decent example math techniques. Showing of 13 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now.
Please try again later. 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 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 lawrencd.
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 dynnamical simpler manner. 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 dynnamical 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 lawrehce 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 didferential 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 syystems are some better texts. There are several textbooks out there which cover this material, but each one differnetial very unique in the systemms 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. 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. 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.
One person found differentiall helpful. This digferential, is one of the best books in ODE’s. It include ststems example the proof od the Hartman Grobman Theorem. Kindle Edition Verified Purchase.
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 ddifferential, 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 dynaical the end of section 1. I was forced to borrow my instructor’s book to finish the homework assignment.
Differential Equations and Dynamical Systems
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 differentiial the textbook is poor or something in between, differenhial 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 ;erko just be stupid? This is an assigned text for my graduate level course.
Overall, I think it is a decent book and covers fair amount of topics, but the impression differentiak I am getting from this book is that it is not written under the presumption that the reader has a strong differehtial in analysis or topology and in that sense it is a tad bit “casual” in certain definitions. My main reservation about this book is that in certain instances the text and sometimes the statements of certain theorems lack clarity and precision, and it takes a rigorous linguistic dissection of the sentences to finally understand what the theorem is saying.
For a math textbook, this flaw is kind of inexcusable. 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 znd 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 differentoal clearer.
A good point are the many exercises, but again, they can contain typos. I would return and demand a refund bu I unfortunately need the book on a daily basis for class. See all 13 reviews. Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more about Amazon Giveaway. Set up a giveaway. Customers who viewed this item also viewed. Theory of Ordinary Differential Equations.
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