The Resource A New Approach to Differential Geometry using Clifford's Geometric Algebra, by John Snygg, (electronic resource)

A New Approach to Differential Geometry using Clifford's Geometric Algebra, by 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
by John Snygg
Creator
Author
Author
Subject
Language
  • eng
  • 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
http://library.link/vocab/creatorName
Snygg, John
Dewey number
  • 512.57
  • 516.3/6
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
syjO5NndH8s
Language note
English
LC call number
QA641-670
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Global differential geometry
  • Mathematical physics
  • Mathematics
  • Algebra
  • Differential Geometry
  • Mathematical Methods in Physics
  • Mathematical Physics
  • Mathematics, general
  • Algebra
  • Applications of Mathematics
Label
A New Approach to Differential Geometry using Clifford's Geometric Algebra, by John Snygg, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 449-458) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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 (471 p.)
Form of item
online
Isbn
9780817682835
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-8283-5
Specific material designation
remote
System control number
  • (CKB)3390000000021135
  • (EBL)973765
  • (OCoLC)826853597
  • (SSID)ssj0000610400
  • (PQKBManifestationID)11347790
  • (PQKBTitleCode)TC0000610400
  • (PQKBWorkID)10638350
  • (PQKB)11368732
  • (DE-He213)978-0-8176-8283-5
  • (MiAaPQ)EBC973765
  • (EXLCZ)993390000000021135
Label
A New Approach to Differential Geometry using Clifford's Geometric Algebra, by John Snygg, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 449-458) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
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 (471 p.)
Form of item
online
Isbn
9780817682835
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-8283-5
Specific material designation
remote
System control number
  • (CKB)3390000000021135
  • (EBL)973765
  • (OCoLC)826853597
  • (SSID)ssj0000610400
  • (PQKBManifestationID)11347790
  • (PQKBTitleCode)TC0000610400
  • (PQKBWorkID)10638350
  • (PQKB)11368732
  • (DE-He213)978-0-8176-8283-5
  • (MiAaPQ)EBC973765
  • (EXLCZ)993390000000021135

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