Symmetries and Differential Equations

  • George W. Bluman
  • Sukeyuki Kumei

Part of the Applied Mathematical Sciences book series (AMS, volume 81)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. George W. Bluman, Sukeyuki Kumei
    Pages 1-3
  3. George W. Bluman, Sukeyuki Kumei
    Pages 4-30
  4. George W. Bluman, Sukeyuki Kumei
    Pages 31-89
  5. George W. Bluman, Sukeyuki Kumei
    Pages 90-162
  6. George W. Bluman, Sukeyuki Kumei
    Pages 163-251
  7. George W. Bluman, Sukeyuki Kumei
    Pages 252-301
  8. George W. Bluman, Sukeyuki Kumei
    Pages 302-351
  9. George W. Bluman, Sukeyuki Kumei
    Pages 352-383
  10. Back Matter
    Pages 384-413

About this book

Introduction

A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.

Keywords

calculus differential equation differential equations lie groups ordinary differential equation partial differential equation symmetry methods

Authors and affiliations

  • George W. Bluman
    • 1
  • Sukeyuki Kumei
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Faculty of Textile Science and TechnologyShinshu UniversityUeda, Nagano 386Japan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4307-4
  • Copyright Information Springer Science+Business Media New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-4309-8
  • Online ISBN 978-1-4757-4307-4
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • About this book