Differential Equations, Dynamical Systems, and an Introduction to Chaos (Anglais) Relié – 26 avril 2012
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Descriptions du produit
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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Commentaires en ligne
Commentaires client les plus utiles sur Amazon.com (beta)
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).
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.
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.