Differential topology and geometry with applications to physics / Eduardo Nahmad-Achar.

Nahmad-Achar, Eduardo, author.
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]
1 online resource (various pagings) : illustrations (some color)
IOP (Series). Release 6.
IOP expanding physics
[IOP release 6]
IOP expanding physics, 2053-2563

Location Notes Your Loan Policy


Geometry, Differential.
Mathematical physics.
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Mode of access: World Wide Web.
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Eduardo Nahmad-Achar earned his BSc in Physics and BSc in Mathematics from the National University of Mexico, and later his MSc in Applied Mathematics and PhD in Physics from the University of Cambridge, UK. He is the author of many scientific publications and has been invited to international conferences to talk about his achievements. He was Founding Director of the Centre for Polymer Research, nr. Mexico City and has lectured extensively at UNAM in various topics of physics and mathematics, including differential geometry, general relativity, advanced mathematics, quantum information, and quantum physics, at both graduate and undergraduate levels.
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.
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.
"Version: 20181201"--Title page verso.
Includes bibliographical references.
Title from PDF title page (viewed on January 16, 2019).
Institute of Physics (Great Britain), publisher.
Other format:
Print version:
Publisher Number:
10.1088/2053-2563/aadf65 doi
Access Restriction:
Restricted for use by site license.