Differential topology and geometry with applications to physics / Eduardo Nahmad-Achar.Material type: TextSeries: IOP (Series). Release 6. | IOP expanding physicsPublisher: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, Description: 1 online resource (various pagings) : illustrations (some color)Content type: text Media type: electronic Carrier type: online resourceISBN: 9780750320726; 9780750320719Subject(s): Geometry, Differential | Topology | Mathematical physics | SCIENCE / Physics / Mathematical & ComputationalAdditional physical formats: Print version:: No titleDDC classification: 516.3/6 LOC classification: QC20.7.D52 | N354 2018ebOnline resources: Click here to access online Also available in print.
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"Version: 20181201"--Title page verso.
Includes bibliographical references.
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.
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.
Also available in print.
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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.
Title from PDF title page (viewed on January 16, 2019).