Introduction To Clifford Analysis

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Introduction to Clifford Analysis

Author : Johan Ceballos
Publisher : Nova Science Publishers
ISBN 13 : 9781536186642
Total Pages : 182 pages
Book Rating : 4.1/5 (866 download)

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Book Synopsis Introduction to Clifford Analysis by : Johan Ceballos

Download or read book Introduction to Clifford Analysis written by Johan Ceballos and published by Nova Science Publishers. This book was released on 2020 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pursues to exhibit how we can construct a Clifford type algebra from the classical one. The basic idea of these lecture notes is to show how to calculate fundamental solutions to either first-order differential operators of the form D=∑_(i=0)^n▒〖e_i δ_i〗or second-order elliptic differential operators ̄D D, both with constant coefficients or combinations of this kind of operators. After considering in detail how to find the fundamental solution we study the problem of integral representations in a classical Clifford algebra and in a dependent-parameter Clifford algebra which generalizes the classical one. We also propose a basic method to extend the order of the operator, for instance D^n,n∈N and how to produce integral representations for higher order operators and mixtures of them. Although the Clifford algebras have produced many applications concerning boundary value problems, initial value problems, mathematical physics, quantum chemistry, among others; in this book we do not discuss these topics as they are better discussed in other courses. Researchers and practitioners will find this book very useful as a source book.The reader is expected to have basic knowledge of partial differential equations and complex analysis. When planning and writing these lecture notes, we had in mind that they would be used as a resource by mathematics students interested in understanding how we can combine partial differential equations and Clifford analysis to find integral representations. This in turn would allow them to solve boundary value problems and initial value problems. To this end, proofs have been described in rigorous detail and we have included numerous worked examples. On the other hand, exercises have not been included.

Clifford Analysis and Its Applications

Author : F. Brackx
Publisher : Springer Science & Business Media
ISBN 13 : 9780792370444
Total Pages : 440 pages
Book Rating : 4.3/5 (74 download)

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Book Synopsis Clifford Analysis and Its Applications by : F. Brackx

Download or read book Clifford Analysis and Its Applications written by F. Brackx and published by Springer Science & Business Media. This book was released on 2001-07-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

Real and Complex Clifford Analysis

Author : Sha Huang
Publisher : Springer Science & Business Media
ISBN 13 : 0387245367
Total Pages : 257 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Real and Complex Clifford Analysis by : Sha Huang

Download or read book Real and Complex Clifford Analysis written by Sha Huang and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors’ investigations, and this new monograph will be interesting for researchers studying the theory of functions.

Introduction to Clifford Analysis

Author : Johan Ceballos
Publisher : Nova Science Publishers
ISBN 13 : 9781536185331
Total Pages : 182 pages
Book Rating : 4.1/5 (853 download)

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Book Synopsis Introduction to Clifford Analysis by : Johan Ceballos

Download or read book Introduction to Clifford Analysis written by Johan Ceballos and published by Nova Science Publishers. This book was released on 2020-10-30 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pursues to exhibit how we can construct a Clifford type algebra from the classical one. The basic idea of these lecture notes is to show how to calculate fundamental solutions to either first-order differential operators of the form D=∑_(i=0)^n▒〖e_i δ_i〗or second-order elliptic differential operators ̄D D, both with constant coefficients or combinations of this kind of operators. After considering in detail how to find the fundamental solution we study the problem of integral representations in a classical Clifford algebra and in a dependent-parameter Clifford algebra which generalizes the classical one. We also propose a basic method to extend the order of the operator, for instance D^n,n∈N and how to produce integral representations for higher order operators and mixtures of them. Although the Clifford algebras have produced many applications concerning boundary value problems, initial value problems, mathematical physics, quantum chemistry, among others; in this book we do not discuss these topics as they are better discussed in other courses. Researchers and practitioners will find this book very useful as a source book.The reader is expected to have basic knowledge of partial differential equations and complex analysis. When planning and writing these lecture notes, we had in mind that they would be used as a resource by mathematics students interested in understanding how we can combine partial differential equations and Clifford analysis to find integral representations. This in turn would allow them to solve boundary value problems and initial value problems. To this end, proofs have been described in rigorous detail and we have included numerous worked examples. On the other hand, exercises have not been included.

Clifford Algebras: An Introduction

Author : D. J. H. Garling
Publisher : Cambridge University Press
ISBN 13 : 1107096383
Total Pages : 209 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Clifford Algebras: An Introduction by : D. J. H. Garling

Download or read book Clifford Algebras: An Introduction written by D. J. H. Garling and published by Cambridge University Press. This book was released on 2011-06-23 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.

Geometric Computing with Clifford Algebras

Author : Gerald Sommer
Publisher : Springer Science & Business Media
ISBN 13 : 3662046210
Total Pages : 559 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Geometric Computing with Clifford Algebras by : Gerald Sommer

Download or read book Geometric Computing with Clifford Algebras written by Gerald Sommer and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics.

Clifford Algebras in Analysis and Related Topics

Author : John Ryan
Publisher : CRC Press
ISBN 13 : 9780849384813
Total Pages : 384 pages
Book Rating : 4.3/5 (848 download)

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Book Synopsis Clifford Algebras in Analysis and Related Topics by : John Ryan

Download or read book Clifford Algebras in Analysis and Related Topics written by John Ryan and published by CRC Press. This book was released on 1995-10-23 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.

An Introduction to Clifford Analysis

Author : J. Cnops
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis An Introduction to Clifford Analysis by : J. Cnops

Download or read book An Introduction to Clifford Analysis written by J. Cnops and published by . This book was released on 1995 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Clifford Algebra to Geometric Calculus

Author : David Hestenes
Publisher : Springer Science & Business Media
ISBN 13 : 9789027725615
Total Pages : 340 pages
Book Rating : 4.7/5 (256 download)

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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 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.

Clifford Algebras and Lie Theory

Author : Eckhard Meinrenken
Publisher : Springer Science & Business Media
ISBN 13 : 3642362168
Total Pages : 331 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Clifford Algebras and Lie Theory by : Eckhard Meinrenken

Download or read book Clifford Algebras and Lie Theory written by Eckhard Meinrenken and published by Springer Science & Business Media. This book was released on 2013-02-28 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.

Higher Order Partial Differential Equations in Clifford Analysis

Author : Elena Obolashvili
Publisher : Springer Science & Business Media
ISBN 13 : 1461200156
Total Pages : 183 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Higher Order Partial Differential Equations in Clifford Analysis by : Elena Obolashvili

Download or read book Higher Order Partial Differential Equations in Clifford Analysis written by Elena Obolashvili and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parabolic equations in this framework have been largely ignored and are the primary focus of this work.; This book will appeal to mathematicians and physicists in PDEs who are interested in boundary and initial value problems, and may be used as a supplementary text by graduate students.

An Introduction to Clifford Algebras and Spinors

Author : Jayme Vaz Jr.
Publisher : Oxford University Press
ISBN 13 : 0198782926
Total Pages : 257 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis An Introduction to Clifford Algebras and Spinors by : Jayme Vaz Jr.

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.

A New Approach to Differential Geometry using Clifford's Geometric Algebra

Author : John Snygg
Publisher : Springer Science & Business Media
ISBN 13 : 081768283X
Total Pages : 472 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A New Approach to Differential Geometry using Clifford's Geometric Algebra by : John Snygg

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.

Quaternion and Clifford Fourier Transforms and Wavelets

Author : Eckhard Hitzer
Publisher : Springer Science & Business Media
ISBN 13 : 3034806035
Total Pages : 338 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Quaternion and Clifford Fourier Transforms and Wavelets by : Eckhard Hitzer

Download or read book Quaternion and Clifford Fourier Transforms and Wavelets written by Eckhard Hitzer and published by Springer Science & Business Media. This book was released on 2013-06-24 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

A Practical Introduction to Data Structures and Algorithm Analysis

Author : Clifford A. Shaffer
Publisher :
ISBN 13 :
Total Pages : 536 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis A Practical Introduction to Data Structures and Algorithm Analysis by : Clifford A. Shaffer

Download or read book A Practical Introduction to Data Structures and Algorithm Analysis written by Clifford A. Shaffer and published by . This book was released on 2001 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical text contains fairly "traditional" coverage of data structures with a clear and complete use of algorithm analysis, and some emphasis on file processing techniques as relevant to modern programmers. It fully integrates OO programming with these topics, as part of the detailed presentation of OO programming itself.Chapter topics include lists, stacks, and queues; binary and general trees; graphs; file processing and external sorting; searching; indexing; and limits to computation.For programmers who need a good reference on data structures.

Clifford Algebras in Analysis and Related Topics

Author : John Ryan
Publisher : CRC Press
ISBN 13 : 1351460277
Total Pages : 174 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Clifford Algebras in Analysis and Related Topics by : John Ryan

Download or read book Clifford Algebras in Analysis and Related Topics written by John Ryan and published by CRC Press. This book was released on 2018-03-09 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.

Clifford (Geometric) Algebras

Author : William E. Baylis
Publisher : Springer Science & Business Media
ISBN 13 : 1461241049
Total Pages : 522 pages
Book Rating : 4.4/5 (612 download)

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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 and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. 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.