Differential Geometry with Applications to Mechanics and Physics
Crc Press Inc (Verlag)
978-0-8247-0385-1 (ISBN)
An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.
Yves Talpaert
Part 1 Topology and differential calculus requirements: topology; differential calculus in Banach spaces; exercises. Part 2 Manifolds: introduction; differential manifolds; differential mappings; submanifolds; exercises. Part 3 Tangent vector space: tangent vector; tangent space; differential at a point; exercises. Part 4 Tangent bundle-vector field-one-parameter group lie algebra: introduction; tangent bundle; vector field on manifold; lie algebra structure; one-parameter group of diffeomorphisms; exercises. Part 5 Cotangent bundle-vector bundle of tensors: cotangent bundle and covector field; tensor algebra; exercises. Part 6 Exterior differential forms: exterior form at a point; differential forms on a manifold; pull-back of a differential form; exterior differentiation; orientable manifolds; exercises. Part 7 Lie derivative-lie group: lie derivative; inner product and lie derivative; Frobenius theorem; exterior differential systems; invariance of tensor fields; lie group and algebra; exercises. Part 8 Integration of forms: n-form integration on n-manifold; integral over a chain; Stokes' theorem; an introduction to cohomology theory; integral invariants; exercises. Part 9 Riemann geometry: Riemannian manifolds.
Erscheint lt. Verlag | 12.9.2000 |
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Reihe/Serie | Chapman & Hall/CRC Pure and Applied Mathematics |
Verlagsort | Bosa Roca |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 907 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Naturwissenschaften ► Physik / Astronomie | |
ISBN-10 | 0-8247-0385-5 / 0824703855 |
ISBN-13 | 978-0-8247-0385-1 / 9780824703851 |
Zustand | Neuware |
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