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Perturbation Methods in Non-Linear Systems

  • Georgio Eugenio Oscare Giacaglia

Part of the Applied Mathematical Sciences book series (AMS, volume 8)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Georgio Eugenio Oscare Giacaglia
    Pages 1-7
  3. Georgio Eugenio Oscare Giacaglia
    Pages 8-54
  4. Georgio Eugenio Oscare Giacaglia
    Pages 55-153
  5. Georgio Eugenio Oscare Giacaglia
    Pages 154-208
  6. Georgio Eugenio Oscare Giacaglia
    Pages 209-273
  7. Georgio Eugenio Oscare Giacaglia
    Pages 274-354
  8. Back Matter
    Pages 355-369

About this book

Introduction

This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ­ ential equations. In this respect, it appears to be a unique work. The main goal is to describe perturbation techniques, discuss their ad­ vantages and limitations and give some examples. The approach is founded on analytical and numerical methods of nonlinear mechanics. Attention has been given to the extension of methods to high orders of approximation, required now by the increased accuracy of measurements in all fields of science and technology. The main theorems relevant to each perturbation technique are outlined, but they only provide a foundation and are not the objective of these notes. Each chapter concludes with a detailed survey of the pertinent literature, supplemental information and more examples to complement the text, when necessary, for better comprehension. The references are intended to provide a guide for background information and for the reader who wishes to analyze any particular point in more detail. The main sources referenced are in the fields of differential equations, nonlinear oscillations and celestial mechanics. Thanks are due to Katherine MacDougall and Sandra Spinacci for their patience and competence in typing these notes. Partial support from the Mathematics Program of the Office of Naval Research is gratefully acknowledged.

Keywords

Lie Perturbation equation mathematics theorem variable

Authors and affiliations

  • Georgio Eugenio Oscare Giacaglia
    • 1
    • 2
  1. 1.University of Sao PauloBrazil
  2. 2.University of Texas at AustinUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-6400-2
  • Copyright Information Springer-Verlag New York 1972
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90054-4
  • Online ISBN 978-1-4612-6400-2
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site
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