Symmetries and Differential Equations

1. Auflage 1989. Corr. 2. printing 1989
ISBN: 978-0-387-96996-1
Verlag: Springer

Buch, Englisch, Band 81, 413 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 645 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Kumei, Sukeyuki

Bluman, George W.

Inhaltsverzeichnis

1 Dimensional Analysis, Modelling, and Invariance.- 2 Lie Groups of Transformations and Infinitesimal Transformations.- 3 Ordinary Differential Equations.- 4 Partial Differential Equations.- 5 Noether’s Theorem and Lie-Bäcklund Symmetries.- 6 Construction of Mappings Relating Differential Equations.- 7 Potential Symmetries.- References.- Author Index.