Mathematical tools
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Bessel function for the drums
Lecturer : Guillame Roux
Syllabus: Course built on miscellaneous small chapters, based on examples. The goal is to recall and/or introduce useful mathematical tools with hands on.
2019-2020: Approximate Schedule for the 13 courses:
- 05/09 Functionals derivatives I -- tutorial -- correction
- 12/09 Functionals derivatives II
- 19/09 Continuous groups and Lie algebra -- notes & tutorial
- 26/09 Complex analysis -- notes & tutorial
- 03/10 Fourier transform + 60min test -- notes & tutorial
- 10/10 Principal value -- tutorial
- 10/10 Kramers-Krönig relations and Gaussian integrals
- 17/10 Wick's theorem, saddle points methods -- tutorial
- 24/10 End of asymptotics expansions + 60min test
- 14/11 Linear algebra -- tutorial
- 21/11 Green's function: static case -- tutorial
- 28/11 Green's function: causality and propagation
- 05/12 Orthogonal polynomials and Special functions -- notes & tutorial
- 08/01 Final Exam (3h) 9:00-12:00, on everything
incomplete bibliography :
- Mathematical Methods for Physicists -- T. L. Chow (free pdf).
- MATHEMATICAL METHODS FOR PHYSICISTS, George B. Arfken & H. J. Weber
- Mathematics for Physics -- M. Stone & P. Goldbart (free pdf)
- Mathematical physics: a modern introduction to its foundations -- S. Hassani
- Mathematical Methods: For Students of Physics and Related Fields -- S. Hassani
- Physics and Mathematical Tools: Methods and Examples -- A. Alastuey, M. Clusel, M. Magro, P. Pujol.
- Group Theory in a Nutshell for Physicists -- Anthony Zee. (if you want to learn group theory)
Evaluation (3 ECTS)
- continuous assessment (1/3 of the final grade): each assessment is graded over 10, this makes a grade over 20. The average grade of the class is typically 14/20.
- final exam : 3 hours, written exam (2/3 of the final grade)
- you are allowed to bring your notes and the distributed documents at the tests and exam, but nothing else.
Previous test
- 2017--2018 : Test on complex calculus -- correction (some typos in modulus squares in the correction...)
- 2018--2019 : Test on complex calculus -- correction
- 2019--2020 : Test on variational calculus -- correction
- 2019--2020 : Test on complex calculus -- correction
Previous final exams
- 2017--2018 : subject -- correction
- 2018--2019 : subject -- correction