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Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering

1996 Mathematics
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Release : 1996
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering by : William Eric Baylis

Download or read book Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering written by William Eric Baylis. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a comprehensive approach to the theoretical, applied and symbolic computational aspects of the subject. Excellent for self-study, leading experts in the field have written on the of topics mentioned above, using an easy approach with efficient geometric language for non-specialists.

Clifford (Geometric) Algebras

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 049/5 ( reviews)

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Book Synopsis Clifford (Geometric) Algebras by : William E. Baylis

Download or read book Clifford (Geometric) Algebras written by William E. Baylis. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.

Applications of Geometric Algebra in Computer Science and Engineering

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 89X/5 ( reviews)

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Book Synopsis Applications of Geometric Algebra in Computer Science and Engineering by : Leo Dorst

Download or read book Applications of Geometric Algebra in Computer Science and Engineering written by Leo Dorst. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Geometric Algebra and Applications to Physics

2006-12-07 Mathematics
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Release : 2006-12-07
Genre : Mathematics
Kind : eBook
Book Rating : 737/5 ( reviews)

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Book Synopsis Geometric Algebra and Applications to Physics by : Venzo de Sabbata

Download or read book Geometric Algebra and Applications to Physics written by Venzo de Sabbata. This book was released on 2006-12-07. Available in PDF, EPUB and Kindle. Book excerpt: Bringing geometric algebra to the mainstream of physics pedagogy, Geometric Algebra and Applications to Physics not only presents geometric algebra as a discipline within mathematical physics, but the book also shows how geometric algebra can be applied to numerous fundamental problems in physics, especially in experimental situations. This

Clifford Algebra to Geometric Calculus

1984-06-30 Science
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Release : 1984-06-30
Genre : Science
Kind : eBook
Book Rating : 730/5 ( reviews)

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Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes

Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes. This book was released on 1984-06-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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