Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications, 1st Edition (Paperback) book cover

Method of Averaging for Differential Equations on an Infinite Interval

Theory and Applications, 1st Edition

By Vladimir Burd

Chapman and Hall/CRC

360 pages | 12 B/W Illus.

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Paperback: 9781584888741
pub: 2007-03-19
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Description

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.

Reviews

". . . a very readable book . . . clearly written book can be highly recommended to students with interests in ordinary differential equations. Non-experts and researchers in natural sciences will also find interesting methods that are useful in applications."

– In EMS Newsletter, March 2008

"Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications."

– in L’Enseignment Math, 2007

Table of Contents

PREFACE

AVERAGING OF LINEAR DIFFERENTIAL EQUATIONS

Periodic and Almost Periodic Functions. Brief Introduction

Bounded Solutions

Lemmas on Regularity and Stability

Parametric Resonance in Linear Systems

Higher Approximations. Shtokalo Method

Linear Differential Equations with Fast and Slow Time

Asymptotic Integration

Singularly Perturbed Equations

AVERAGING OF NONLINEAR SYSTEMS

Systems in Standard Form. First Approximation

Systems in Standard Form. First Examples

Pendulum Systems with an Oscillating Pivot

Higher Approximations of the Method of Averaging

Averaging and Stability

Systems with a Rapidly Rotating Phase

Systems with a Fast Phase. Resonant Periodic Oscillations

Systems with Slowly Varying Parameters

APPENDICES

Almost Periodic Functions

Stability of the Solutions of Differential Equations

Some Elementary Facts from the Functional Analysis

REFERENCES

INDEX

About the Series

Lecture Notes in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis