Clifford Algebra To Geometric Calculus

Author : David Hestenes
Publisher : Springer Science & Business Media
ISBN 13 : 9789027725615
Total Pages : 340 pages
Book Rating : 4.16/5 ( download)

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Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. 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 Algebra' 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 quaternions, 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.

Author : David Hestenes
Publisher : Springer
ISBN 13 : 9027716730
Total Pages : 314 pages
Book Rating : 4.36/5 ( download)

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Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer. This book was released on 1984-06-30 with total page 314 pages. 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.

Author : John Snygg
Publisher : Springer Science & Business Media
ISBN 13 : 081768283X
Total Pages : 472 pages
Book Rating : 4.35/5 ( download)

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Download or read book A New Approach to Differential Geometry using Clifford's Geometric Algebra written by John Snygg and published by Springer Science & Business Media. This book was released on 2011-12-09 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Alan Macdonald
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781480132450
Total Pages : 0 pages
Book Rating : 4.54/5 ( download)

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Download or read book Vector and Geometric Calculus written by Alan Macdonald and published by Createspace Independent Publishing Platform. This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. This is the printing of August 2022. The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/ macdonal/laga. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it. Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/ macdonal/vagc. From a review of Linear and Geometric Algebra: Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers. -- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College

Author : D. Hestenes
Publisher : Springer Science & Business Media
ISBN 13 : 9400962924
Total Pages : 332 pages
Book Rating : 4.27/5 ( download)

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Download or read book Clifford Algebra to Geometric Calculus written by D. Hestenes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. 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.

Author : David Hestenes
Publisher :
ISBN 13 :
Total Pages : 314 pages
Book Rating : 4.33/5 ( download)

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Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by . This book was released on 1984 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : William Eric Baylis
Publisher : Boston : Birkhäuser
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.54/5 ( download)

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Download or read book Clifford (geometric) Algebras with Applications to Physics, Mathematics, and Engineering written by William Eric Baylis and published by Boston : Birkhäuser. This book was released on 1996 with total page 544 pages. 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.

Author : John Vince
Publisher : Springer Science & Business Media
ISBN 13 : 1846289963
Total Pages : 268 pages
Book Rating : 4.65/5 ( download)

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Download or read book Geometric Algebra for Computer Graphics written by John Vince and published by Springer Science & Business Media. This book was released on 2008-04-21 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems. The author tackles this complex subject with inimitable style, and provides an accessible and very readable introduction. The book is filled with lots of clear examples and is very well illustrated. Introductory chapters look at algebraic axioms, vector algebra and geometric conventions and the book closes with a chapter on how the algebra is applied to computer graphics.

Author : John W. Arthur
Publisher : John Wiley & Sons
ISBN 13 : 0470941634
Total Pages : 320 pages
Book Rating : 4.38/5 ( download)

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Download or read book Understanding Geometric Algebra for Electromagnetic Theory written by John W. Arthur and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison. Professors can request a solutions manual by email: [email protected]

Author : Jayme Vaz Jr.
Publisher : Oxford University Press
ISBN 13 : 0198782926
Total Pages : 257 pages
Book Rating : 4.26/5 ( download)

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Download or read book An Introduction to Clifford Algebras and Spinors written by Jayme Vaz Jr. and published by Oxford University Press. This book was released on 2016 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.