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The Resource A new approach to differential geometry using Clifford's geometric algebra, John Snygg

A new approach to differential geometry using Clifford's geometric algebra, John Snygg

Label
A new approach to differential geometry using Clifford's geometric algebra
Title
A new approach to differential geometry using Clifford's geometric algebra
Statement of responsibility
John Snygg
Creator
Subject
Language
eng
Summary
Differential geometry is the study of curvature and calculus of curves and surfaces. Because of an historical accident, the Geometric Algebra devised by William Kingdom Clifford (1845-1879) has been overlooked in favor of the more complicated and less powerful formalism of differential forms and tangent vectors to deal with differential geometry. Fortuitously a student who has completed an undergraduate course in linear algebra is better prepared to deal with the intricacies of Clifford algebra than with the formalism currently used. Clifford algebra enables one to demonstrate a close relation between curvature and certain rotations. This is an advantage both conceptually and computationally-particularly in higher dimensions. Key features and topics include: * a unique undergraduate-level approach to differential geometry; * brief biographies of historically relevant mathematicians and physicists; * some aspects of special and general relativity accessible to undergraduates with no knowledge of Newtonian physics; * chapter-by-chapter exercises. The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginning-level graduate students; researchers in the algebra and physics communities may also find the book useful as a self-study guide
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Snygg, John
Dewey number
516.3/6
Illustrations
illustrations
Index
index present
LC call number
QA641
LC item number
.S69 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Geometry, Differential
  • Clifford algebras
  • Clifford algebras
  • Geometry, Differential
Label
A new approach to differential geometry using Clifford's geometric algebra, John Snygg
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 449-458) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Introduction -- Clifford Algebra in Euclidean 3-Space -- Clifford Algebra in Minkowski 4-Space -- Clifford Algebra in Flat n-Space -- Curved Spaces -- The Gauss-Bonnet Formula -- Non-Euclidean (Hyperbolic) Geometry -- Some Extrinsic Geometry in Ên -- Ruled Surfaces Continued -- Lines of Curvature -- Minimal Surfaces -- Some General Relativity -- Matrix Representation of a Clifford Algebra -- Construction of Coordinate Dirac Matrices -- A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets -- A Few Terms of the Taylor's Series for Kepler's Orbits -- References -- Index
Control code
769755408
Dimensions
unknown
Extent
1 online resource (xvii, 465 pages)
File format
unknown
Form of item
online
Isbn
9780817682835
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)769755408
Label
A new approach to differential geometry using Clifford's geometric algebra, John Snygg
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 449-458) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Introduction -- Clifford Algebra in Euclidean 3-Space -- Clifford Algebra in Minkowski 4-Space -- Clifford Algebra in Flat n-Space -- Curved Spaces -- The Gauss-Bonnet Formula -- Non-Euclidean (Hyperbolic) Geometry -- Some Extrinsic Geometry in Ên -- Ruled Surfaces Continued -- Lines of Curvature -- Minimal Surfaces -- Some General Relativity -- Matrix Representation of a Clifford Algebra -- Construction of Coordinate Dirac Matrices -- A Few Terms of the Taylor's Series for the Urdī-Copernican Model for the Outer Planets -- A Few Terms of the Taylor's Series for Kepler's Orbits -- References -- Index
Control code
769755408
Dimensions
unknown
Extent
1 online resource (xvii, 465 pages)
File format
unknown
Form of item
online
Isbn
9780817682835
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)769755408

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