The Resource The method of equivalence and its applications, Robert B. Gardner, (electronic resource)

The method of equivalence and its applications, Robert B. Gardner, (electronic resource)

Label
The method of equivalence and its applications
Title
The method of equivalence and its applications
Statement of responsibility
Robert B. Gardner
Title variation
Equivalence and its applications
Creator
Contributor
Publisher
Subject
Language
eng
Summary
The ideas of Elie Cartan are combined with the tools of Felix Klein and Sophus Lie to present in this book the only detailed treatment of the method of equivalence. An algorithmic description of this method, which finds invariants of geometric objects under infinite dimensional pseudo-groups, is presented for the first time. As part of the algorithm, Gardner introduces several major new techniques. In particular, the use of Cartan's idea of principal components that appears in his theory of Repere Mobile, and the use of Lie algebras instead of Lie groups, effectively a linear procedure, provide a tremendous simplification. One must, however, know how to convert from one to the other, and the author provides the Rosetta stone to accomplish this. In complex problems, it is essential to be able to identify natural blocks in group actions and not just individual elements, and prior to this publication, there was no reference to block matrix techniques. The Method of Equivalence and Its Applications details ten diverse applications including Lagrangian field theory, control theory, ordinary differential equations, and Riemannian and conformal geometry. This volume contains a series of lectures, the purpose of which was to describe the equivalence algorithm and to show, in particular, how it is applied to several pedagogical examples and to a problem in control theory called state estimation of plants under feedback. The lectures, and hence the book, focus on problems in real geometry
Member of
Cataloging source
CaBNVSL
http://library.link/vocab/creatorName
Gardner, Robert B
Illustrations
illustrations
Index
no index present
LC call number
QA649
LC item number
.G36 1989eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Society for Industrial and Applied Mathematics
Series statement
CBMS-NSF regional conference series in applied mathematics
Series volume
58
http://library.link/vocab/subjectName
  • Geometry, Differential
  • Invariants
  • Transformations (Mathematics)
Target audience
adult
Label
The method of equivalence and its applications, Robert B. Gardner, (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references
Color
black and white
Contents
Equivalence problems -- Lifting of equivalence problems to G-spaces -- The structure equations -- Reduction of the structure group by normalization -- The inductive step -- e-structures -- Global results and involutive structure -- Serendipity -- Normal forms and generalized geometries -- Prolongation
Dimensions
unknown
Extent
1 online resource (vii, 127 p.)
File format
multiple file formats
Form of item
online
Isbn
9781611970135
Other physical details
ill.
Reformatting quality
access
Specific material designation
remote
System control number
  • (CaBNVSL)gtp00547322
  • (SIAM)9781611970135
Label
The method of equivalence and its applications, Robert B. Gardner, (electronic resource)
Publication
Bibliography note
Includes bibliographical references
Color
black and white
Contents
Equivalence problems -- Lifting of equivalence problems to G-spaces -- The structure equations -- Reduction of the structure group by normalization -- The inductive step -- e-structures -- Global results and involutive structure -- Serendipity -- Normal forms and generalized geometries -- Prolongation
Dimensions
unknown
Extent
1 online resource (vii, 127 p.)
File format
multiple file formats
Form of item
online
Isbn
9781611970135
Other physical details
ill.
Reformatting quality
access
Specific material designation
remote
System control number
  • (CaBNVSL)gtp00547322
  • (SIAM)9781611970135

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