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[[File:Bessel.gif|200px|thumb|[https://en.wikipedia.org/wiki/Bessel_function Bessel function] for the drums]]
[[File:Bessel.gif|200px|thumb|[https://en.wikipedia.org/wiki/Bessel_function Bessel function] for the drums]]


* '''tutor''' : Guillame Roux
'''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.
'''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''' :
Schedule for the 13 courses:
** [http://www.worldscientific.com/worldscibooks/10.1142/9733 Physics and Mathematical Tools: Methods and Examples] -- A. Alastuey, M. Clusel, M. Magro, P. Pujol.
* 07/09 Functionals derivatives I
** [http://physics.bgu.ac.il/~gedalin/Teaching/Mater/mmp.pdf Mathematical Methods for Physicists] -- T. L. Chow (free pdf).
* 14/09 Functionals derivatives II
** [https://www.elsevier.com/books/mathematical-methods-for-physicists/arfken/978-0-12-384654-9 MATHEMATICAL METHODS FOR PHYSICISTS], George B. Arfken & H. J. Weber
* 21/09 Lagrange multipliers and functional integration
** [www.goldbart.gatech.edu/PostScript/MS_PG_book/bookmaster.pdf Mathematics for Physics] -- M. Stone & P. Goldbart
* 28/09 Complex analysis + '''30min test on 1.2.3'''
** Group Theory in a Nutshell for Physicists -- Anthony Zee.
* 05/10 Fourier transform
* 12/10 Linear response and Kramers-Krönig relations
* 19/10 Gaussian integrals
* 26/10 Steepest descent + '''30min test on 4.5.6.7'''
* 02/11 Linear algebra
* 16/11 Landau-Zener formula
* 23/11 Orthogonal polynomials
* 30/11 Green's function
* 07/12 Differential geometry
* 21/12 '''3h Exam''' on everything (date to be confirmed)


* '''Evaluation''' (3 ECTS)
'''incomplete bibliography''' :
** a few exercices during the tutorials
* [http://www.worldscientific.com/worldscibooks/10.1142/9733 Physics and Mathematical Tools: Methods and Examples] -- A. Alastuey, M. Clusel, M. Magro, P. Pujol.
** final exam : 3 hours, written exam
* [http://physics.bgu.ac.il/~gedalin/Teaching/Mater/mmp.pdf Mathematical Methods for Physicists] -- T. L. Chow (free pdf).
* [https://www.elsevier.com/books/mathematical-methods-for-physicists/arfken/978-0-12-384654-9 MATHEMATICAL METHODS FOR PHYSICISTS], George B. Arfken & H. J. Weber
* [http://www.goldbart.gatech.edu/PostScript/MS_PG_book/bookmaster.pdf Mathematics for Physics] -- M. Stone & P. Goldbart
* [https://press.princeton.edu/titles/10773.html Group Theory in a Nutshell for Physicists] -- Anthony Zee.
 
'''Evaluation''' (3 ECTS)
* continuous assessment
* final exam : 3 hours, written exam

Revision as of 16:38, 5 October 2017

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.

Schedule for the 13 courses:

  • 07/09 Functionals derivatives I
  • 14/09 Functionals derivatives II
  • 21/09 Lagrange multipliers and functional integration
  • 28/09 Complex analysis + 30min test on 1.2.3
  • 05/10 Fourier transform
  • 12/10 Linear response and Kramers-Krönig relations
  • 19/10 Gaussian integrals
  • 26/10 Steepest descent + 30min test on 4.5.6.7
  • 02/11 Linear algebra
  • 16/11 Landau-Zener formula
  • 23/11 Orthogonal polynomials
  • 30/11 Green's function
  • 07/12 Differential geometry
  • 21/12 3h Exam on everything (date to be confirmed)

incomplete bibliography :

Evaluation (3 ECTS)

  • continuous assessment
  • final exam : 3 hours, written exam
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