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Clifford Algebra to Geometric Calculus

A Unified Language for Mathematics and Physics

  • David Hestenes
  • Garret Sobczyk

Part of the Fundamental Theories of Physics book series (FTPH, volume 5)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. David Hestenes, Garret Sobczyk
    Pages 1-43
  3. David Hestenes, Garret Sobczyk
    Pages 44-62
  4. David Hestenes, Garret Sobczyk
    Pages 63-136
  5. David Hestenes, Garret Sobczyk
    Pages 137-187
  6. David Hestenes, Garret Sobczyk
    Pages 188-224
  7. David Hestenes, Garret Sobczyk
    Pages 225-248
  8. David Hestenes, Garret Sobczyk
    Pages 249-282
  9. David Hestenes, Garret Sobczyk
    Pages 283-304
  10. Back Matter
    Pages 305-314

About this book

Introduction

Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

Keywords

Fundamental theorem of calculus Vector space algebra derivative differential equation geometry mathematics transformation

Authors and affiliations

  • David Hestenes
    • 1
  • Garret Sobczyk
    • 2
  1. 1.Department of PhysicsArizona State UniversityUSA
  2. 2.Institute for Theoretical PhysicsUniversity of WrocławPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-6292-7
  • Copyright Information Springer Science+Business Media B.V. 1984
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-277-2561-5
  • Online ISBN 978-94-009-6292-7
  • Buy this book on publisher's site
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