Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications: 255 (Lecture Notes in Pure and Applied Mathematics) - Softcover

Burd, Vladimir

Softcover

ISBN 10: 1584888741 ISBN 13: 9781584888741

Publisher: Chapman and Hall/CRC, 2007

Synopsis

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 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 Shtokalo's 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 Banfi's 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.

About this title

About the Author

Vladimir Burd

From the Back Cover

Method of Averaging of the Infinite Interval: Theory and Applications provides a thorough understanding of this theory and its resulting applications. The first part of the book is devoted to the theory of averaging linear differential equations that have almost periodic coefficients. The second part focuses on nonlinear equations, addressing standard form systems as well as systems with a fast rotating phase. The book contains exercises to help with the study of applied problems. It also includes appendices with useful facts about almost periodic functions, stability theory, and functional analysis.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2007
• Language: English
• ISBN 10: 1584888741
• ISBN 13: 9781584888741
• Binding: Paperback
• Edition number: 1
• Number of pages: 356