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Clifford algebra to geometric calculus : a unified language for mathematics and physics

Author: David Hestenes; Garret Sobczyk
Publisher: Dordrecht ; Boston : D. Reidel ; Hingham, MA, U.S.A. : Distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 1985, ©1984.
Series: Fundamental theories of physics.
Edition/Format:   Print book : English : Reprinted with correctionsView all editions and formats
Database:WorldCat
Summary:
Geometric Calculus is a language for expressing and analyzing the full range of geometric concepts in mathematics. Clifford Algebra provides the grammar. Complex number, quaternions, matrix algebra, vector, tensor and spinor calculus and differential forms are integrated into a single comprehensive system. The geometric calculus developed in this book has the following features: a systematic development of  Read more...
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Document Type: Book
All Authors / Contributors: David Hestenes; Garret Sobczyk
ISBN: 9027716730 9789027716736
OCLC Number: 13505489
Description: xviii, 314 pages ; 25 cm.
Contents: Preface --
Introduction --
1. Geometric algebra --
2. Differentiation --
3. Linear and multilinear functions --
4. Calculus on vector manifolds --
5. Differential geometry of vector manifolds --
6. The method of mobiles --
7. Directed integration theory --
8. Lie groups and Lie algebras.
Series Title: Fundamental theories of physics.
Other Titles: Geometric calculus
Responsibility: by David Hestenes and Garret Sobczyk.
More information:

Abstract:

Geometric Calculus is a language for expressing and analyzing the full range of geometric concepts in mathematics. Clifford Algebra provides the grammar. Complex number, quaternions, matrix algebra, vector, tensor and spinor calculus and differential forms are integrated into a single comprehensive system. The geometric calculus developed in this book has the following features: a systematic development of definitions, concepts and theorems needed to apply the calculus easily and effectively to almost any branch of mathematics or physics; a formulation of linear algebra capable of details computations without matrices or coordinates; new proofs and treatments of canonical forms including an extensive discussion of spinor representations of rotations in Euclidean n-space; a new concept of differentiation which makes it possible to formulate calculus on manifolds and carry out complete calculations of such thinks as the Jacobian of a transformation without resorting to coordinates; a coordinate-free approach to differential geometry featuring a new quantity, the shape tensor, from which the curvature tensor can be computed without a connection; a formulation of integration theory based on a concept of directed measure, with new results including a generalization of Cauchy's integral formula to n-dimension spaces and explicit integral formula for the inverse of a transformation; a new approach to Lie groups and Lie algebras. --From cover.

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'... future authors will owe a great debt to Professors Hestenes and Sobczyk for this pioneering work.' Foundations of Physics, 16, 1986 'I repeat that GC enriches and simplifies everything it Read more...

 
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