附註:"This book is a significant update of the first four chapters of Symmetries and differential equations, Springer 1989 (reprinted with corrections 1996), by George W. Bluman and Sukeyuki Kumei"--Preface.
Includes bibliographical references (pages 391-400) and indexes.
Preface -- Introduction -- Dimensional Analysis, Modelling, and Invariance -- Lie Groups of Transformations and Infinitesimal Transformations -- Ordinary Differential Equations -- Partial Differential Equations -- Noether's Theorem and Lie-B cklund Symmetries -- Construction of Mappings Relating Differential Equations -- Potential Symmetries -- References -- Author Index -- Subject Index.
摘要:This book provides a comprehensive treatment of symmetry methods and dimensional analysis. The authors discuss aspects of Lie groups of point transformations, contact symmetries, and higher order symmetries that are essential for solving differential equations. Emphasis is given to an algorithmic, computational approach to finding integrating factors and first integrals. Numerous examples including ordinary differential equations arising in applied mathematics are used for illustration and exercise sets are included throughout the text. This book is designed for advanced undergraduate or beginning graduate students of mathematics and physics, as well as researchers in mathematics, physics, and engineering.
