Ordinary Differential Equations (Dover Books on Mathematics) by Prof. Jack K. Hale (PDF)

Description

Based on a Brown University course in applied mathematics, this rigorous and demanding treatment focuses on specific analytical methods. It emphasizes nonlinear problems, acquainting readers with problems and techniques in ordinary differential equations. The material is presented in a manner that prepares students for informed research of differential equations, teaching them how to be more effective in studies of the current literature. In addressing the applied side of the subject, the text devotes considerable attention to specific analytical methods common to applications. Introductory chapters offer necessary background material by reviewing basic facts of analysis and covering the general properties of differential equations. Topics include two-dimensional systems, linear systems and linearization, perturbations of noncritical linear systems, simple oscillatory phenomena and the method of averaging, and behavior near a periodic orbit. Additional subjects include integral manifolds of equations with a small parameter, periodic systems with a small parameter, alternative problems for the solution of functional equations, and the direct method of Liapunov. Exercises appear at the end of each chapter, and the appendix contains a convenient reference for almost every periodic functions.

User’s Reviews

Editorial Reviews: About the Author A longtime professor at Brown University, Jack K. Hale is a Regents Professor Emeritus at the Georgia Institute of Technology.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The unique problem is the fontsize of the characters. The characters are very, very short and it’s difficult to read even for those who need wear glasses. But the content is very good. Dover Publications should make a new version of this book increasing the text font size.

⭐very good quality, better than new paperback ones!

⭐I studied this book many years ago as a graduate student, it was the textbook for the ODEs course at that time. it belongs to those ODEs books which avoids references to PDE so it is an ODE book aiming to dynamical systems. Its content is not pedagogically distributed so it is a relatively hard book to learn from it. Moreover, it is a little bit outdated, so I would say that it is a four star book

⭐Despite being only about 300 pages, Hale’s “Ordinary Differential Equations” contains a wealth of information. The emphasis is definitely on nonlinear problems, and in this respect, the book is excellent, as it focuses very much on analytical techniques for analyzing such problems. Perturbation and averaging methods are abundant, and proofs are rigorous. Most importantly, the reader will learn the standard arguments used in proving such results. The text is also useful as a reference on linear systems, especially periodic linear systems. Standard topics including Poincaré-Benedixson theory and stable/unstable manifolds are also present.The treatment is certainly demanding; suggested exercises are often posed vaguely. Hale wants you to read the question, think for a while and figure out what he’s REALLY asking, and then do some analysis. This is both a good and a bad thing, since the problems may lead to more insight, but diminish the usefulness of the text as a reference.I use this book so often, after renewing it about four times from my university’s library, I purchased my own copy. And with it being so cheap, why not?The font is definitely small, though. However, it probably wouldn’t be a problem unless you required corrective lenses for reading.

⭐This book it’s pretty much oriented for a graduate level student in Mathematics, personally, I would use it as a reference rather than a main lecture book for a course.The proofs are rigorous, and the pacing it’s appropriate if not somewhat “alternative” to what is used to today.My main concern is the font, which is a bit too small for someone with glasses, but as I like to say, the book is just packed up with information.Excelente texto para todo aquel que desea seguuf en el camino de las ecuaciones diferenciales, sistemas dinámicos y la teoría de control.no puedo opinar, me censuran los censores de amazon.estutto OK

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