What is classical math
Mathematical Physics: Classical Mechanics
- The students know basic concepts and methods of differential geometry, symplectic geometry and dynamic systems.
- The students know the applications of these concepts and methods in classical mechanics.
- The students safely apply the concepts and methods they have learned in the context of sample tasks and can transfer them to related contexts.
- Using the example of classical mechanics, the students recognize how mathematical physics deals with questions from physics from the perspective of mathematics.
- Differential geometric basics, e.g. manifolds, tangential bundles, flows, tensors
- Symplectic geometry
- Dynamical systems, especially Hamiltonian systems, e.g. the theorem of Liouville and Arnold
- Perturbation theory, KAM theorem
- 13.02.2017, 9: 00-10: 30, S11
A discussion forum has been set up at https://forum.zdv.uni-tuebingen.de for a continuous exchange of information about lectures and exercises. You can log in there with your ZDV login.
The lecture is not based on a single book. The following books are suitable for accompanying reading.
- R. Abraham, J.E. Marsden, Foundations of Mechanics, 2nd ed., Benjamin Cummings, Reading, 1978.
- V.I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed., Springer, New York, 1989.
- A. Knauf, Mathematical Physics: Classical Mechanics, Springer, Heidelberg, 2012.
- F. check, mechanics, 2nd edition, Springer, Berlin, 1990.
- N. Straumann, Classic mechanics, Springer, Berlin, 1987.
- W. Thirring, Textbook of Mathematical Physics 1 - Classical Dynamical Systems, Springer, Vienna, 1977.
- Differential geometry
- J. Baez, J.P. Muniain, Gauge Fields, Knots and Gravity, World Scientific, Singapore, 1961.
- T. Frankel, The Geometry of Physics, Cambridge University Press, Cambridge, 1997.
- M. Nakahara, Geometry, Topology and Physics, IOP Publishing, 1990.
- C. Nash, S. Sen, Topology and Geometry for Physicists, Academic Press, London, 1983.
- G. Rudolph, M. Schmidt, Differential Geometry and Mathematical Physics, Springer, Dodrecht, 2013.
- Dynamic systems
- A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
- Basics (differential and integral calculation in R.n)
- M. Spivak, Calculus on manifolds, W.A. Benjamin, Menlo Park, CA, 1965.
- W. Rudin, Principles of Mathematical Analysis, 2nd ed., McGraw-Hill, New York, 1964, [especially Chap. 9].
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