Symmetries and Differential Equations

George W. Bluman, Sukeyuki Kumei (Autoren)

Buch | Hardcover

413 Seiten

1989
Springer-Verlag New York Inc.
978-0-387-96996-1 (ISBN)

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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.

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.

Erscheint lt. Verlag	25.4.1996
Reihe/Serie	Applied Mathematical Sciences ; 81
Zusatzinfo	XIII, 413 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-387-96996-9 / 0387969969
ISBN-13	978-0-387-96996-1 / 9780387969961
Zustand	Neuware