Mathematical tools

Bessel function for the drums

• tutor : 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.
  • Functionals : derivation, integration and constraints.
  • Matrices : exponential, determinants.
  • Around the gaussian, steepest descent method.
  • Hilbert spaces, linear operators, distributions, orthogonal polynomials.
  • Complex analysis : analycity, calculus.
  • Differential equations : Green's function, method of characteristics, non-linear examples.
  • Differential geometry : line, surface, volume, curvature, orthogonal coordinates.
  • Functions : homogeneous functions, some special functions.
  • Elements of group theory.

• incomplete bibliography :
  • Physics and Mathematical Tools: Methods and Examples -- A. Alastuey, M. Clusel, M. Magro, P. Pujol.
  • Mathematical Methods for Physicists -- T. L. Chow.
  • Mathematics for Physics -- M. Stone & P. Goldbart
  • MATHEMATICAL METHODS FOR PHYSICISTS, George B. Arfken & H. J. Weber
  • Group Theory in a Nutshell for Physicists -- Anthony Zee.

• Evaluation (3 ECTS)
  • a few exercices during the tutorials
  • final exam : 3 hours, written exam