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, 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].