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Differential Equations, Dynamical Systems, and an Introduction to Chaos (Anglais) Relié – 26 avril 2012

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Présentation de l'éditeur

Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.

  • Classic text by three of the world’s most prominent mathematicians
  • Continues the tradition of expository excellence
  • Contains updated material and expanded applications for use in applied studies

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20 internautes sur 20 ont trouvé ce commentaire utile 
Excellent 5 novembre 2012
Par ubpdqn - Publié sur Amazon.com
Format: Format Kindle
I read this book quicker than I wanted to. It will be a wonderful resource to come back with the explorations and the exercises. As such this review pertains to reading rather than getting the most out of this book. This limitation aside, this is a very clearly written and illustrated book.

There is a progressive increase in complexity proceeding from one dimensional linear autonomous differential equations, to linearisation of non-linear equation, qualitative assessments through analysis of equilibrium points, Poincare maps. The section introducing chaos (focussing on hallmarks of density of periodic orbits, transitivity and sensitivity to initial conditions) is very interesting. I found the chaotic behaviour of logistic map and relation (homeomorphism) to Cantor sets very interesting.

It is a very good textbook and I look forward to a time when I can maximize my learning by diving into the explorations (esp. with Mathematica).
4 internautes sur 4 ont trouvé ce commentaire utile 
The sweet spot 23 septembre 2014
Par David B. Borenstein - Publié sur Amazon.com
Format: Format Kindle
I have been using this book for years. I wish I could get into some of the specifics that I found most useful, but I lent it to a student and they never gave it back. That makes sense--this book saved my bacon when I took an innocuously named "Applied Dynamical Systems" class (ha!), and the "borrower" can be forgiven for needing it equally much. I found that the descriptions, and particularly the illustrations, provided more detail than Strogatz, and with greater brevity, without assuming an excess of knowledge. It is also vastly gentler than, say, Guckenheimer & Holmes, and has much more information than Hale.

At the time that I read this book, I had only taken an introductory class on ODEs, and a pretty light one at that. With some googling and supplemental exercises, I got through the material alright. I particularly appreciated the useful examples, which I still find myself consulting now and then, especially while preparing for lectures. I highly recommend it.
4 internautes sur 54 ont trouvé ce commentaire utile 
Doesn't explain much. 4 février 2013
Par James Waddington - Publié sur Amazon.com
Format: Format Kindle
The main issue is that this book would leave many things undefined. It would mention things like bifurcation points, phase lines, but would never define them. Multiple times during reading it I had to look up terms in other sources to get definitions. Granted this isn't necessarily a show stopper, but when words are bold-faced it's more or less expected that they are to be defined. Often times you had to guess what something was in a diagram to get something close to a definition.

This book was part of the reason why I dropped a math class I had planned on taking. Granted I had only read the first chapter, before giving up on it, so as far as I know it gets better after the chapter. On an unrelated note the publisher is known for being quite sleazy with their business practices, so that might be another reason not to use this book.
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