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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)
Resource Information
The item A new approach to differential geometry using Clifford's geometric algebra, John Snygg, (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 A new approach to differential geometry using Clifford's geometric algebra, John Snygg, (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
 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 undergraduatelevel 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; * chapterbychapter exercises. The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginninglevel graduate students; researchers in the algebra and physics communities may also find the book useful as a selfstudy guide
 Language
 eng
 Extent
 1 online resource (xvii, 465 p.)
 Contents

 Preface
 Introduction
 Clifford Algebra in Euclidean 3Space
 Clifford Algebra in Minkowski 4Space
 Clifford Algebra in Flat nSpace
 Curved Spaces
 The GaussBonnet Formula
 NonEuclidean (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 UrdīCopernican Model for the Outer Planets
 A Few Terms of the Taylor's Series for Kepler's Orbits
 References
 Index
 Isbn
 9780817682835
 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
 Subject

 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Differential Geometry
 Electronic resources
 Geometry, Differential
 Geometry, Differential
 Geometry, Differential
 Algebra
 Geometry, Differential
 Geometry, Differential
 Geometry, Differential
 Geometry, Differential
 Global differential geometry
 Mathematical Methods in Physics
 Mathematical physics
 Mathematics
 Mathematics, general
 Geometry, Differential
 Applications of Mathematics
 Clifford algebras
 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 undergraduatelevel 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; * chapterbychapter exercises. The textbook will also serve as a useful classroom resource primarily for undergraduates as well as beginninglevel graduate students; researchers in the algebra and physics communities may also find the book useful as a selfstudy 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)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (p. 449458) and index
 Color
 not applicable
 Contents
 Preface  Introduction  Clifford Algebra in Euclidean 3Space  Clifford Algebra in Minkowski 4Space  Clifford Algebra in Flat nSpace  Curved Spaces  The GaussBonnet Formula  NonEuclidean (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 UrdīCopernican 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)
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (p. 449458) and index
 Color
 not applicable
 Contents
 Preface  Introduction  Clifford Algebra in Euclidean 3Space  Clifford Algebra in Minkowski 4Space  Clifford Algebra in Flat nSpace  Curved Spaces  The GaussBonnet Formula  NonEuclidean (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 UrdīCopernican 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
Subject
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Clifford algebras
 Differential Geometry
 Electronic resources
 Geometry, Differential
 Geometry, Differential
 Geometry, Differential
 Algebra
 Geometry, Differential
 Geometry, Differential
 Geometry, Differential
 Geometry, Differential
 Global differential geometry
 Mathematical Methods in Physics
 Mathematical physics
 Mathematics
 Mathematics, general
 Geometry, Differential
 Applications of Mathematics
 Clifford algebras
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