Differential Geometry : Basic Notions and Physical Examples / by Marcelo Epstein

By:

Epstein, Marcelo [aut]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Mathematical Engineering | SpringerLink BücherPublisher: Cham ; s.l. : Springer International Publishing, 2014Description: Online-Ressource (XI, 139 p. 26 illus, online resource)ISBN:

9783319069203

Subject(s):

Additional physical formats: 9783319069197 | Erscheint auch als: Differential geometry. Druck-Ausgabe Cham : Springer, 2014. XI, 139 S.DDC classification:

516.36

MSC: MSC: *53-01 | 53C80 | 53Z05RVK: RVK: SK 370LOC classification:

QA641-670

DOI: DOI: 10.1007/978-3-319-06920-3Online resources:

Contents:

Topological constructsPhysical illustrations -- Differential constructs -- Physical illustrations.

Summary: Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics. Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media. Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory. This book will be useful for researchers and graduate students in science and engineeringPPN: PPN: 1658933281Package identifier: Produktsigel: ZDB-2-ENG

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