Cantitate/Preț
Produs

Differential Geometry and Lie Groups: A Second Course: Geometry and Computing, cartea 13

Autor Jean Gallier, Jocelyn Quaintance
en Limba Engleză Paperback – 19 aug 2021
This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.  Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications.

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.
Citește tot Restrânge

Toate formatele și edițiile

Toate formatele și edițiile Preț Express
Paperback (2) 43211 lei  6-8 săpt.
  Springer International Publishing – 19 aug 2021 43211 lei  6-8 săpt.
  Springer International Publishing – 16 aug 2021 45890 lei  38-44 zile
Hardback (2) 45929 lei  38-44 zile
  Springer International Publishing – 19 aug 2020 45929 lei  38-44 zile
  Springer International Publishing – 15 aug 2020 47353 lei  38-44 zile

Din seria Geometry and Computing

Preț: 43211 lei

Nou

Puncte Express: 648

Preț estimativ în valută:
8270 8590$ 6869£

Carte tipărită la comandă

Livrare economică 03-17 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9783030460495
ISBN-10: 3030460495
Pagini: 620
Ilustrații: XIV, 620 p. 110 illus., 32 illus. in color.
Dimensiuni: 155 x 235 x 36 mm
Greutate: 0.88 kg
Ediția:1st ed. 2020
Editura: Springer International Publishing
Colecția Springer
Seria Geometry and Computing

Locul publicării:Cham, Switzerland

Cuprins

1. Tensor Algebras.- 2. Exterior Tensor Powers and Exterior Algebras.- 3. Differential Forms.- 4. Distributions and the Frobenius Theorem.- 5. Integration on Manifolds.- 6. Spherical Harmonics and Linear Representations.- 7. Operators on Riemannian Manifolds.- 8. Bundles, Metrics on Bundles, Homogeneous Spaces.- 9. Connections and Curvature in Vector Bundles.- 10. Clifford Algebras, Clifford Groups, Pin and Spin.

Notă biografică

Jean Gallier is Professor of Computer and Information Science at the University of Pennsylvania, Philadelphia. His research interests include geometry and its applications, geometric modeling, and differential geometry. He is also a member of the University of Pennsylvania’s Department of Mathematics, and its Center for Human Modelling and Simulation.

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.

Textul de pe ultima copertă

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing.  Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications.

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 algebraicconclusion, 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.

Caracteristici

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

Recenzii

“The book … is intended ‘for a wide audience ranging from upper undergraduate to advanced graduate students in mathematics, physics, and more broadly engineering students, especially in computer science.’ …  The text’s coverage is extensive, its exposition clear throughout, and the color illustrations helpful. The authors are also familiar with many texts at a comparable level and have drawn on them in several places to include some of the most insightful proofs already in the literature.” (Jer-Chin Chuang, MAA Reviews, October 4, 2021)

“The book is intended for incremental study and covers both basic concepts and more advanced ones. The former are thoroughly supported with theory and examples, and the latter are backed up with extensive reading lists and references. … Thanks to its design and approach style this is a timely and much needed addition that enables interdisciplinary bridges and the discovery of new applications for differential geometry.” (Corina Mohorian, zbMATH 1453.53001, 2021)