Introduction to Clifford Algebra
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| Title: | Introduction to Clifford Algebra |
|---|---|
| Description: | 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. |
| Authors: | Johan Ceballos |
| Resource Type: | eBook. |
| Subjects: | Clifford algebras |
| Categories: | MATHEMATICS / Algebra / General |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Introduction to Clifford Algebra – Name: Abstract Label: Description Group: Ab Data: 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. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Johan+Ceballos%22">Johan Ceballos</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Clifford+algebras%22">Clifford algebras</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+General%22">MATHEMATICS / Algebra / General</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512.57 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Clifford algebras Type: general Titles: – TitleFull: Introduction to Clifford Algebra Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Johan Ceballos – PersonEntity: Name: NameFull: Johan Ceballos IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2020 – D: 12 M: 09 Type: profile Y: 2024 Identifiers: – Type: isbn-print Value: 9781536185331 – Type: isbn-electronic Value: 9781536186642 Titles: – TitleFull: Introduction to Clifford Algebra Type: main |
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