9780521101042

Equivalence, Invariants and Symmetry

by
  • ISBN13:

    9780521101042

  • ISBN10:

    0521101042

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2009-02-05
  • Publisher: Cambridge University Press
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Summary

This book presents an innovative synthesis of methods used to study the problems of equivalence and symmetry that arise in a variety of mathematical fields and physical applications. It draws on a wide range of disciplines, including geometry, analysis, applied mathematics, and algebra. Dr. Olver develops systematic and constructive methods for solving equivalence problems and calculating symmetries, and applies them to a variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials, and differential operators. He emphasizes the construction and classification of invariants and reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and related fields.

Table of Contents

Geometric foundations
Lie groups
Representation theory
Jets and contact transformations
Differential invariants
Symmetries of differential equations
Symmetries of variational problems
Equivalence of coframes
Formulation of equivalence problems
Cartan's equivalence method
Involution
Prolongation of equivalence problems
Differential systems
Frobenius' theorem
The Cartanndash;Kahler existence theorem
Table of Contents provided by Publisher. All Rights Reserved.

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