Mathematical tools

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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