# What is classical math

## Mathematical Physics: Classical Mechanics

- info

**learning goals**

- 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.

**Content**

- 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

**Exam**

**13.02.2017**, 9: 00-10: 30, S11

**Web forum**

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.

### Bibliography

The lecture is not based on a single book. The following books are suitable for accompanying reading.

**mechanics**- R. Abraham, J.E. Marsden,
*Foundations of Mechanics,*2^{nd}ed., Benjamin Cummings, Reading, 1978. - V.I. Arnold,
*Mathematical Methods of Classical Mechanics*, 2^{nd}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.

- R. Abraham, J.E. Marsden,
**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.

- J. Baez, J.P. Muniain,
**Dynamic systems**- A. Katok, B. Hasselblatt,
*Introduction to the Modern Theory of Dynamical Systems*, Cambridge University Press, Cambridge, 1995.

- A. Katok, B. Hasselblatt,
**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*, 2^{nd}ed., McGraw-Hill, New York, 1964, [especially Chap. 9].

- M. Spivak,

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