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Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions.
Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors¿ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions.
Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors¿ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
Jocelyn Quaintance is postdoctoral researcher at the University of Pennsylvania who has contributed to the fields of combinatorial identities and power product expansions. Her recent mathematical books investigate the interplay between mathematics and computer science. Covering areas as diverse as differential geometry, linear algebra, optimization theory, and Fourier analysis, her writing illuminates the mathematics behind topics relevant to engineering, computer vision, and robotics.
Explores the advanced mathematical theory behind modern geometry processing
Offers a uniquely accessible approach that is suitable for students and professionals alike
Augments core topics in advanced differential geometry with analytic and algebraic perspectives
Includes exercises throughout that are suitable for class use or independent study
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 636 |
| Reihe: | Geometry and Computing |
| Inhalt: |
xiv
620 S. 78 s/w Illustr. 32 farbige Illustr. 620 p. 110 illus. 32 illus. in color. |
| ISBN-13: | 9783030460464 |
| ISBN-10: | 3030460460 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Quaintance, Jocelyn
Gallier, Jean |
| Auflage: | 1st ed. 2020 |
| Hersteller: |
Springer International Publishing
Geometry and Computing |
| Maße: | 241 x 160 x 38 mm |
| Von/Mit: | Jocelyn Quaintance (u. a.) |
| Erscheinungsdatum: | 19.08.2020 |
| Gewicht: | 1,225 kg |
Jocelyn Quaintance is postdoctoral researcher at the University of Pennsylvania who has contributed to the fields of combinatorial identities and power product expansions. Her recent mathematical books investigate the interplay between mathematics and computer science. Covering areas as diverse as differential geometry, linear algebra, optimization theory, and Fourier analysis, her writing illuminates the mathematics behind topics relevant to engineering, computer vision, and robotics.
Explores the advanced mathematical theory behind modern geometry processing
Offers a uniquely accessible approach that is suitable for students and professionals alike
Augments core topics in advanced differential geometry with analytic and algebraic perspectives
Includes exercises throughout that are suitable for class use or independent study
| Erscheinungsjahr: | 2020 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 636 |
| Reihe: | Geometry and Computing |
| Inhalt: |
xiv
620 S. 78 s/w Illustr. 32 farbige Illustr. 620 p. 110 illus. 32 illus. in color. |
| ISBN-13: | 9783030460464 |
| ISBN-10: | 3030460460 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Quaintance, Jocelyn
Gallier, Jean |
| Auflage: | 1st ed. 2020 |
| Hersteller: |
Springer International Publishing
Geometry and Computing |
| Maße: | 241 x 160 x 38 mm |
| Von/Mit: | Jocelyn Quaintance (u. a.) |
| Erscheinungsdatum: | 19.08.2020 |
| Gewicht: | 1,225 kg |
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