Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications, Volume 255 Vladimir Burd

ISBN: 9781281274786

Published: January 10th 2010

ebook

343 pages


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Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications, Volume 255  by  Vladimir Burd

Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications, Volume 255 by Vladimir Burd
January 10th 2010 | ebook | PDF, EPUB, FB2, DjVu, audiobook, mp3, RTF | 343 pages | ISBN: 9781281274786 | 3.60 Mb

In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method ofMoreIn recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications.

Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory. The book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions.

It describes stability theory and Shtokalos method, and examines various applications, including parametric resonance and the construction of asymptotics. After establishing this foundation, the author goes on to explore nonlinear equations. He studies standard form systems in which the right-hand side of a system is proportional to a small parameter and proves theorems similar to Banfis theorem.

The final chapters are devoted to systems with a rapidly rotating phase. Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications.



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