Differentiable manifolds: a theoretical physics approach
by Torres del Castillo, G. F., (Gerardo Francisco)
This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations…
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- Full title :Differentiable manifolds : a theoretical physics approach / Gerardo F. Torres del Castillo.
Summary
This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations, connections, Riemannian manifolds, Lie groups, and Hamiltonian mechanics. Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics. This second edition greatly expands upon the first by including more examples, additional exercises, and new topics, such as the moment map and fiber bundles. Detailed solutions to every exercise are also provided.
Read More ↓Edition Statements
- Publication Date:©2020
- Edition:2nd ed
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Cham
- Language:eng
- Publication Date:©2020
The Physical Object
- Description:1 online resource (x, 444 pages)
Edition Identifiers
- ISBN:9783030451936, 3030451933
- oclc:on1162846259
- LC Classification:QA614.3
- Dewey Decimal:516.3/6
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