A Practical Guide to the Invariant Calculus

by Elizabeth Louise Mansfield

Overview

This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.

Product Details

ISBN-13:	9780521857017
Publisher:	Cambridge University Press
Publication date:	04/29/2010
Series:	Cambridge Monographs on Applied and Computational Mathematics , #26
Pages:	260
Product dimensions:	6.10(w) x 9.00(h) x 0.70(d)

About the Author

Elizabeth Louise Mansfield is Professor of Mathematics at the University of Kent, Canterbury.

Table of Contents

Preface; Introduction to invariant and equivariant problems; 1. Actions galore; 2. Calculus on Lie groups; 3. From Lie group to Lie algebra; 4. Moving frames; 5. On syzygies and curvature matrices; 6. Invariant ordinary differential equations; 7. Variational problems with symmetry; References; Index.

Editorial Reviews

"This book is full of good examples. Mansfield is clearly in love with the subject; her enthusiasm is apparent. While learning about moving frames is still not easy, this book helps, especially if the reader follows the advice of the author when she writes, "How to read this book... is with pencil and paper, and symbolic computation software. The only way to see the magic is to do it."
Thomas Garrity, Mathematical Reviews

From the Publisher