Equivalence, invariants, and symmetry
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Bibliographic Information
Equivalence, invariants, and symmetry
Cambridge University Press, 2008
- : pbk
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Note
"This digitally printed version 2008"--T.p. verso
Originally published: 1995
Includes bibliographical references (p. [477]-489) and indexes
Description and Table of Contents
Description
Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the 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 other related fields.
Table of Contents
- 1. Geometric foundations
- 2. Lie groups
- 3. Representation theory
- 4. Jets and contact transformations
- 5. Differential invariants
- 6. Symmetries of differential equations
- 7. Symmetries of variational problems
- 8. Equivalence of coframes
- 9. Formulation of equivalence problems
- 10. Cartan's equivalence method
- 11. Involution
- 12. Prolongation of equivalence problems
- 13. Differential systems
- 14. Frobenius' theorem
- 15. The Cartan-Kahler existence theorem.
by "Nielsen BookData"