A Practical Guide To the Invariant Calculus by Elizabeth Louise Mansfield

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Caspian Outlet

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.

Book Description
Moving frames explained in the language of undergraduate calculus, suitable for graduate students. –This text refers to the hardcover edition.
Review
“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
Book Description
This book explains and develops new applications of continuous symmetry groups (Lie groups), in particular, the symbolic manipulation of invariants of group actions. The language used is primarily that of undergraduate calculus. More sophisticated ideas from differential topology and Lie theory are explained from scratch using worked examples and exercises.
About the Author
Elizabeth Louise Mansfield is Professor of Mathematics at the University of Kent, Canterbury.

Product Key Features
Format Hardcover
Language English
Publication Year 2010
Number of Pages 260 Pages

Dimensions
Item Length 9.2in.
Item Height 0.7in.
Item Width 6.2in.
Item Weight 19.4 Oz

Author Elizabeth Louise Mansfield
Table of Content 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.
Copyright Date 2010
Target Audience Scholarly & Professional
Topic Differential Equations / General, Geometry / Differential, Topology
Lccn 2010-281917
Dewey Decimal 512.55
Series Cambridge Monographs ON Applied and Computational Mathematics Ser.
Dewey Edition 22
Illustrated Yes
Genre Mathematics

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