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Differential topology and geometry with applications to physics

Author: Eduardo Nahmad-Achar; Institute of Physics (Great Britain),
Publisher: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]
Series: IOP expanding physics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Eduardo Nahmad-Achar; Institute of Physics (Great Britain),
ISBN: 9780750320726 0750320729 9780750320719 0750320710
OCLC Number: 1082881976
Notes: "Version: 20181201"--Title page verso.
Description: 1 online resource : illustrations (some color).
Contents: 1. Synopsis of general relativity --
2. Curves and surfaces in E3 --
3. Elements of topology --
4. Differentiable manifolds --
5. Tangent vectors and tangent spaces --
6. Tensor algebra --
7. Tensor fields and commutators --
8. Differential forms and exterior calculus --
9. Maps between manifolds --
10. Integration on manifolds --
11. Integral curves and Lie derivatives --
12. Linear connections --
13. Geodesics --
14. Torsion and curvature --
15. Pseudo-Riemannian metric --
16. Newtonian space-time and thermodynamics --
17. Special relativity, electrodynamics, and the Poincaré group --
18. General relativity --
19. Gravitational radiation --
20. Further reading.
Series Title: IOP expanding physics.
Responsibility: Eduardo Nahmad-Achar.

Abstract:

Differential geometry has encountered numerous applications in physics. More and more physical concepts can be understood as a direct consequence of geometric principles. The mathematical structure of Maxwell's electrodynamics, of the general theory of relativity, of string theory, and of gauge theories, to name but a few, are of a geometric nature. All of these disciplines require a curved space for the description of a system, and we require a mathematical formalism that can handle the dynamics in such spaces if we wish to go beyond a simple and superficial discussion of physical relationships. This formalism is precisely differential geometry. Even areas like thermodynamics and fluid mechanics greatly benefit from a differential geometric treatment. Not only in physics, but in important branches of mathematics has differential geometry effected important changes. Aimed at graduate students and requiring only linear algebra and differential and integral calculus, this book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry together with essential applications in many branches of physics.

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