Fr. 108.00

A New Approach to Differential Geometry using Clifford's Geometric Algebra

Englisch · Fester Einband

2-3 Tage

Beschreibung

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Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.

Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Inhaltsverzeichnis

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 Urdi-Copernican Model for the Outer Planets.- A Few Terms of the Taylor's Series for Kepler's Orbits.- References.- Index.

Zusammenfassung

Differential geometry is the study of the curvature and calculus of curves and surfaces. The conceptual complications introduced by a multitude of spaces and mappings normally required in the study of differential geometry usually postpones the topic to graduate-level courses. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an undergraduate level of differential geometry by introducing Clifford algebra. This presentation is relevant since Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.
 
Key features include:
 
·         a rare undergraduate-level approach to differential geometry;
·         brief biographies of historically relevant mathematicians and physicists;
·         significant aspects of general relativity and Riemannian geometry and
·         chapter-by-chapter exercises. 
This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

 
This accessible and comprehensive textbook offers a valuable introduction to differential geometry, simplifying the complicated theory by using Clifford algebra. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

Zusatztext

From the reviews:
“The book is written in a very pedagogical style and seems to be the mirror of the original ideas of its author in the area of mathematical physics. … The typography is excellent and the figures are beautiful. … Graduate and advanced undergraduate students in physics and even in mathematics will find in this book an understanding of the contribution of Clifford algebras to the field of differential geometry as well as motivation to continue their study.” (Pierre Anglès, Mathematical Reviews, March, 2014)
“The book under review is perfectly organized textbook for undergraduate students in mathematics and physics due to the large experience of the author. … The author provides quite interesting historical analysis … . This book is a natural continuation of the previous book of the author … .” (Milen Hristov, JGSP Journal of Geometry and Symmetry in Physics, Vol. 33, 2014)
“The author develops the differential geometry of curves and surfaces by using Clifford’s geometric algebra. … The book is enriched with several very interesting and extensive historical and biographical presentations. … it can serve as an accompanying source for someone who studies differential geometry, or for someone who wants to look at known facts from a different viewpoint. Also, it is ideal for studying geometry through historical development, and thus this book could also be useful for reading courses on certain aspects of geometry.” (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1232, 2012)

Bericht

From the reviews:

"The book is written in a very pedagogical style and seems to be the mirror of the original ideas of its author in the area of mathematical physics. ... The typography is excellent and the figures are beautiful. ... Graduate and advanced undergraduate students in physics and even in mathematics will find in this book an understanding of the contribution of Clifford algebras to the field of differential geometry as well as motivation to continue their study." (Pierre Anglès, Mathematical Reviews, March, 2014)

"The book under review is perfectly organized textbook for undergraduate students in mathematics and physics due to the large experience of the author. ... The author provides quite interesting historical analysis ... . This book is a natural continuation of the previous book of the author ... ." (Milen Hristov, JGSP Journal of Geometry and Symmetry in Physics, Vol. 33, 2014)

"The author develops the differential geometry of curves and surfaces by using Clifford's geometric algebra. ... The book is enriched with several very interesting and extensive historical and biographical presentations. ... it can serve as an accompanying source for someone who studies differential geometry, or for someone who wants to look at known facts from a different viewpoint. Also, it is ideal for studying geometry through historical development, and thus this book could also be useful for reading courses on certain aspects of geometry." (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1232, 2012)

Produktdetails

Autoren John Snygg
Verlag Springer, Basel
 
Thema Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Geometrie
Sprache Englisch
Produktform Fester Einband
Erschienen 01.12.2011
 
EAN 9780817682828
ISBN 978-0-8176-8282-8
Seiten 465
Abmessung 159 mm x 243 mm x 33 mm
Gewicht 822 g
Illustration 102 SW-Abb.

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