| 书目名称 | Similarity Methods for Differential Equations | | 编辑 | G. W. Bluman,J. D. Cole | | 视频video | | | 丛书名称 | Applied Mathematical Sciences | | 图书封面 |  | | 描述 | The aim of this book is to provide a systematic and practical account of methods of integration of ordinary and partial differential equations based on invariance under continuous (Lie) groups of trans formations. The goal of these methods is the expression of a solution in terms of quadrature in the case of ordinary differential equations of first order and a reduction in order for higher order equations. For partial differential equations at least a reduction in the number of independent variables is sought and in favorable cases a reduction to ordinary differential equations with special solutions or quadrature. In the last century, approximately one hundred years ago, Sophus Lie tried to construct a general integration theory, in the above sense, for ordinary differential equations. Following Abel‘s approach for algebraic equations he studied the invariance of ordinary differential equations under transformations. In particular, Lie introduced the study of continuous groups of transformations of ordinary differential equations, based on the infinitesimal properties of the group. In a sense the theory was completely successful. It was shown how for a first-order differential eq | | 出版日期 | Book 1974 | | 关键词 | Finite; Invariant; Lie; algebra; calculus; equation; function; ordinary differential equation; partial diffe | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-6394-4 | | isbn_softcover | 978-0-387-90107-7 | | isbn_ebook | 978-1-4612-6394-4Series ISSN 0066-5452 Series E-ISSN 2196-968X | | issn_series | 0066-5452 | | copyright | Springer-Verlag New York Inc. 1974 |
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发表于 2025-3-21 19:09:21
