Differential Equations with Small Parameters and Relaxation Oscillations (Mathematical Concepts and Methods in Science and Engineering)

E. Mishchenko

ISBN 10: 1461590493 / ISBN 13: 9781461590491

Published by Springer 1980-12-01, 1980

About this Item

Seller Inventory # 6666-IUK-9781461590491

Bibliographic Details

• Title: Differential Equations with Small Parameters and Relaxation Oscillations (Mathematical Concepts and Methods in Science and Engineering)
• Publisher: Springer 1980-12-01
• Publication Date: 1980
• Language: English
• ISBN 10: 1461590493
• ISBN 13: 9781461590491
• Binding: Paperback
• Condition: New

About this title

Synopsis

A large amount of work has been done on ordinary differ- ential equations with small parameters multiplying deriv- atives. This book investigates questions related to the asymptotic calculation of relaxation oscillations, which are periodic solutions formed of sections of both sl- and fast-motion parts of phase trajectories. A detailed discussion of solutions of differential equations involving small parameters is given for regions near singular points. The main results examined were obtained by L. S. Pontryagin and the authors. Other works have also been taken into account: A. A. Dorodnitsyn's investigations of Van der Pol's equation, results obtained by N. A. Zheleztsov and L. V. Rodygin concerning relaxation oscillations in electronic devices, and results due to A. N. Tikhonov and A. B. Vasil'eva concerning differential equations with small parameters multiplying certain derivatives. E. F. Mishchenko N. Kh. Rozov v CONTENTS Chapter I. Dependence of Solutions on Small Parameters. Applications of Relaxation Oscillations 1. Smooth Dependence. Poincare's Theorem . 1 2. Dependence of Solutions on a Parameter, on an Infinite Time Interval 3 3. Equations with Small Parameters 4 Multiplying Derivatives 4. Second-Order Systems. Fast and Slow Motion.

Language Notes

Text: English, Russian (translation)