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

A new approach to differential geometry using Clifford's geometric algebra, John Snygg, (electronic resource)

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
Contributor
Provider
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
Image bit depth
0
LC call number
QA641
LC item number
.S69 2012
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
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, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Bibliography note
Includes bibliographical references (p. 449-458) and index
Color
not applicable
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 E^n -- 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
Dimensions
unknown
Extent
1 online resource (xvii, 465 p.)
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9780817682835
Level of compression
uncompressed
Other physical details
ill.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (OCoLC)769755408
  • (OCoLC)ocn769755408
Label
A new approach to differential geometry using Clifford's geometric algebra, John Snygg, (electronic resource)
Publication
Antecedent source
mixed
Bibliography note
Includes bibliographical references (p. 449-458) and index
Color
not applicable
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 E^n -- 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
Dimensions
unknown
Extent
1 online resource (xvii, 465 p.)
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9780817682835
Level of compression
uncompressed
Other physical details
ill.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (OCoLC)769755408
  • (OCoLC)ocn769755408

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