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Physik-Institut

PHY312 Mathematical Methods of Physics I

General Information

Lecturer: Prof. Massimiliano Grazzini
Assistants:

Dr. Daniel Baranowski - Y36 K30

Flavio Guadagni - Y36 K36

Markus Löchner - Y36 K74

Jan-Niklas Toelstede - Y36 H70 and PSI
Lectures: Tuesday, 13:00 - 14:45, in Y03 G91
Thursday, 13:00 - 14:45, in Y03 G91
Exercises: Friday, 8:00 - 10:00, in Y16 G05
Tutoring: Monday, 15.00-17:00, in Y36 J33
OLAT: Exercise sheets will be handled through the OLAT page of the course

Exam:

January 12,  2024, 9.00-12.00, Y16 G05

Help

3 sheets (6 pages) A4 personal notes allowed, no electronic device

Mock Exam

December 22, 2023, 8.00-11.00, Y34 K02
  • In order to pass the Module three conditions have to be fulfilled: i) 60% of the exercises assigned during the course must be delivered and carried out correctly; ii) the student must go at least once at the blackboard to solve the assigned exercise iii) the final exam must be passed.

Announcements

The first lecture will be on Thursday September 21, 2023 at 13.00 in Y03 G91. The first exercise class will be on Friday September 29, 2023 at 8.00 in Y16 G05.

Lecture notes

  1. Complex Analysis: Introduction (PDF, 1 MB)
  2. Cauchy Theorem (PDF, 933 KB)
  3. Cauchy Integral Formula (PDF, 776 KB)
  4. Laurent Series and the Residue Theorem (PDF, 782 KB)
  5. Analytic continuation (PDF, 950 KB)
  6. Conformal Mapping (PDF, 325 KB)
  7. Distributions (PDF, 470 KB)
  8. Fourier Series (PDF, 582 KB)
  9. Fourier Transformation (PDF, 1 MB)
  10. Ordinary Differential Equations (PDF, 395 KB)
  11. Systems of first-order ODEs and higher-order ODEs (PDF, 1 MB)
  12. Laplacian and Schroedinger equation (PDF, 435 KB)
  13. Poisson and Laplace equations, Dirichlet problem, Green functions (PDF, 353 KB)

Bibliography

  • M.J. Ablowitz and A.S.Fokas, Complex Variables: Introduction and Applications, Cambridge 2003
  • G.B. Arfken and H.J. Weber, Mathematical Methods for Physicists, Academic Press, Inc. 1995
  • S. Hassani, Mathematical Physics, A Modern Introduction to its Foundations, Springer
  • Group Theory in Physics, Wu-Ki Tung, World Scientific
  • H. Cartan, Elementare Theorien der Analytischen Funktionen einer oder mehreren Komplexen Veränderlichen, BI Hochschultaschenbücher Band 112, 1966
  • S. Lang, Complex Analysis, Springer Verlag 1993
  • L. V. Ahlfors, Complex Analysis 2nd ed. 1966
  • J. F. Cornwell, Group Theory in Physics, Academic Press 1984