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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)
Resource Information
The item The method of equivalence and its applications, Robert B. Gardner, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item The method of equivalence and its applications, Robert B. Gardner, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 pseudogroups, 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
 Language
 eng
 Extent
 1 online resource (vii, 127 p.)
 Contents

 Equivalence problems
 Lifting of equivalence problems to Gspaces
 The structure equations
 Reduction of the structure group by normalization
 The inductive step
 estructures
 Global results and involutive structure
 Serendipity
 Normal forms and generalized geometries
 Prolongation
 Isbn
 9781611970135
 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
 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 pseudogroups, 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
 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
 CBMSNSF 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)
 Bibliography note
 Includes bibliographical references
 Color
 black and white
 Contents
 Equivalence problems  Lifting of equivalence problems to Gspaces  The structure equations  Reduction of the structure group by normalization  The inductive step  estructures  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)
 Bibliography note
 Includes bibliographical references
 Color
 black and white
 Contents
 Equivalence problems  Lifting of equivalence problems to Gspaces  The structure equations  Reduction of the structure group by normalization  The inductive step  estructures  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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/Themethodofequivalenceanditsapplications/4hm9gqwDzMY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/Themethodofequivalenceanditsapplications/4hm9gqwDzMY/">The method of equivalence and its applications, Robert B. Gardner, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>