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The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes¿s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.
The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.
The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes¿s theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics.
The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.
Andreas Rosén is a Professor at the Chalmers University of Technology and the University of Gothenburg, Sweden. His research mostly concerns Partial Differential Equations, and uses techniques from harmonic analysis and operator theory.
Develops carefully the foundations of calculus of multivector fields and differential forms
Explains advanced material in a self-contained and down-to-earth way, e.g. Clifford algebra, spinors, differential forms and index theorems
Touches on modern research areas in analysis
Contains a novel treatment of Hodge decompositions based on first-order differential operators
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Birkhäuser Advanced Texts Basler Lehrbücher |
| Inhalt: |
xiii
465 S. 21 s/w Illustr. 8 farbige Illustr. 465 p. 29 illus. 8 illus. in color. |
| ISBN-13: | 9783030314132 |
| ISBN-10: | 3030314138 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Rosén, Andreas |
| Auflage: | 1st ed. 2019 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing Springer International Publishing AG Birkhäuser Advanced Texts Basler Lehrbücher |
| Maße: | 235 x 155 x 26 mm |
| Von/Mit: | Andreas Rosén |
| Erscheinungsdatum: | 20.11.2020 |
| Gewicht: | 0,721 kg |
Andreas Rosén is a Professor at the Chalmers University of Technology and the University of Gothenburg, Sweden. His research mostly concerns Partial Differential Equations, and uses techniques from harmonic analysis and operator theory.
Develops carefully the foundations of calculus of multivector fields and differential forms
Explains advanced material in a self-contained and down-to-earth way, e.g. Clifford algebra, spinors, differential forms and index theorems
Touches on modern research areas in analysis
Contains a novel treatment of Hodge decompositions based on first-order differential operators
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Birkhäuser Advanced Texts Basler Lehrbücher |
| Inhalt: |
xiii
465 S. 21 s/w Illustr. 8 farbige Illustr. 465 p. 29 illus. 8 illus. in color. |
| ISBN-13: | 9783030314132 |
| ISBN-10: | 3030314138 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Rosén, Andreas |
| Auflage: | 1st ed. 2019 |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing Springer International Publishing AG Birkhäuser Advanced Texts Basler Lehrbücher |
| Maße: | 235 x 155 x 26 mm |
| Von/Mit: | Andreas Rosén |
| Erscheinungsdatum: | 20.11.2020 |
| Gewicht: | 0,721 kg |
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