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Applied Mathematical Sciences #81: Symmetry and Integration Methods for Differential Equationsby George W. Bluman
Synopses & Reviews
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.
This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.
Table of Contents
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.
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