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Lectures on Clifford (Geometric) Algebras and Applications
1 online resource (xvii, 221 pages 25 illustrations)
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird's-eye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field. Key topics and features of this systematic exposition: * An Introductory chapter on Clifford Algebras by Pertti Lounesto * Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups * John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the well-known complex analysis of the plane to three and higher dimensions * William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity * John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and bi-quaternions, have found in computer vision and robotics * Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry * Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, on-line calculators, special purpose numeric software, and symbolic add-ons to computer algebra systems This text will serve beginning graduate students and researchers in diverse areas---mathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications.
Preface / Rafał Abłamowicz, Garret Sobczyk -- Lecture 1: Introduction to Clifford algebras / Pertti Lounesto -- Lecture 2: Mathematical structure of Clifford algebras / Ian Porteous -- Lecture 3: Clifford analysis / John Ryan -- Lecture 4: Applications of Clifford algebras in physics / William E. Baylis -- Lecture 5: Clifford algebras in engineering / J.M. Selig -- Lecture 6: Clifford bundles and Clifford algebras / Thomas Branson -- Appendix / Rafał Abłamowicz, Garret Sobczyk.
by Rafal Ablamowicz, William E. Baylis, Thomas Branson, Pertti Lounesto, Ian Porteous, John Ryan, J.M. Selig, Garret Sobczyk ; edited by Rafal Abłamowicz, Garret Sobczyk.
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Includes bibliographical references and index.