Introduction To Clifford Analysis PDF Download
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Author | : Johan Ceballos |
Publisher | : Nova Science Publishers |
Total Pages | : 182 |
Release | : 2020-10-30 |
Genre | : |
ISBN | : 9781536185331 |
Download Introduction to Clifford Analysis Book in PDF, ePub and Kindle
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.
Author | : Sha Huang |
Publisher | : Springer Science & Business Media |
Total Pages | : 257 |
Release | : 2006-03-16 |
Genre | : Mathematics |
ISBN | : 0387245367 |
Download Real and Complex Clifford Analysis Book in PDF, ePub and Kindle
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.
Author | : J. Cnops |
Publisher | : |
Total Pages | : 86 |
Release | : 1995 |
Genre | : Clifford algebras |
ISBN | : |
Download An Introduction to Clifford Analysis Book in PDF, ePub and Kindle
Author | : Swanhild Bernstein |
Publisher | : Springer Nature |
Total Pages | : 503 |
Release | : 2019-10-15 |
Genre | : Mathematics |
ISBN | : 3030238547 |
Download Topics in Clifford Analysis Book in PDF, ePub and Kindle
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
Author | : F. Brackx |
Publisher | : Springer Science & Business Media |
Total Pages | : 440 |
Release | : 2001-07-31 |
Genre | : Mathematics |
ISBN | : 9780792370444 |
Download Clifford Analysis and Its Applications Book in PDF, ePub and Kindle
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.
Author | : D. J. H. Garling |
Publisher | : Cambridge University Press |
Total Pages | : 209 |
Release | : 2011-06-23 |
Genre | : Mathematics |
ISBN | : 1107096383 |
Download Clifford Algebras: An Introduction Book in PDF, ePub and Kindle
A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.
Author | : John Ryan |
Publisher | : CRC Press |
Total Pages | : 384 |
Release | : 1995-10-23 |
Genre | : Mathematics |
ISBN | : 9780849384813 |
Download Clifford Algebras in Analysis and Related Topics Book in PDF, ePub and Kindle
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.
Author | : Jan Cnops |
Publisher | : |
Total Pages | : |
Release | : 1995 |
Genre | : |
ISBN | : |
Download An Introduction to Clifford Analysis Book in PDF, ePub and Kindle
Author | : Jayme Vaz Jr. |
Publisher | : Oxford University Press |
Total Pages | : 257 |
Release | : 2016 |
Genre | : Mathematics |
ISBN | : 0198782926 |
Download An Introduction to Clifford Algebras and Spinors Book in PDF, ePub and Kindle
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.
Author | : David Hestenes |
Publisher | : Springer Science & Business Media |
Total Pages | : 340 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 9789027725615 |
Download Clifford Algebra to Geometric Calculus Book in PDF, ePub and Kindle
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.