Symmetries and differential equations
Symmetries and differential equations
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DOI：
10.1007/978-1-4757-4307-4
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
G. Bluman;S. Kumei
中科院分区：
文献类型：
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作者：
G. Bluman;S. Kumei
这本书的主要部分讨论了自从第一作者和JD Cole于1974年出版了《微分方程的相似方法》一书以来所出现的工作。本书还包括李群变换的彻底和全面的处理，以及它们在解常微分方程式和偏微分方程式中的各种用途。不假定对群论有任何了解。重点放在显式计算算法上，以发现微分方程所允许的对称性并构造由对称性产生的解。这本书应该特别适合物理学家、应用数学家和工程师。几乎所有的例子都取自物理和工程问题，包括与热传导、波传播和流体流动有关的问题。第一作者在1987-88年间在不列颠哥伦比亚大学为应用数学和物理专业的研究生和大四本科生讲授了一门为期两学期的课程，课程的初稿被用作课堂笔记。第一章到第四章涵盖了基本材料。更专门的主题将在第5章至第7章中介绍。
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 JD 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.