UID:
almahu_9948201686802882
Format:
1 online resource (various pagings) :
,
illustrations (some color).
ISBN:
9780750320726
,
9780750320719
Series Statement:
[IOP release 6]
Content:
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.
Note:
"Version: 20181201"--Title page verso.
,
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.
,
Also available in print.
,
Mode of access: World Wide Web.
,
System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Additional Edition:
Print version: ISBN 9780750320702
Language:
English
DOI:
10.1088/2053-2563/aadf65
URL:
https://iopscience.iop.org/book/978-0-7503-2072-6
