Mathematical tools

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.

Approximate Schedule for the 13 courses:

• ??/09 Functionals derivatives I -- tutorial
• ??/09 Functionals derivatives II
• ??/09 Lagrange multipliers and functional integration
• ??/09 Complex analysis + 30min test on 1.2.3 -- tutorial
• ??/10 Fourier transform -- tutorial
• ??/10 Principal value -- tutorial
• ??/10 Kramers-Krönig relations
• ??/10 Gaussian integrals + 60min test on 4.5.6.7
• ??/11 Wick's theorem -- tutorial
• ??/11 Saddle points methods
• ??/11 Linear algebra -- tutorial
• ??/11 Green's function: static case -- tutorial
• ??/12 Green's function: causality and propagation
• ??/01 Final Exam (3h) 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
• final exam : 3 hours, written exam