Mathematical tools: Difference between revisions

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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
'''Master''' : an option of the Master 2 [https://physics-complex-systems.fr/ Physics of complex system]


* '''Syllabus''': Course built on miscellaneous small chapters, based on examples. The goal is to recall and/or introduce useful mathematical tools with hands on.
'''Lecturer''' : [http://lptms.u-psud.fr/membres/groux/index.html Guillame Roux]
** 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''' :
'''Syllabus''': Course built on miscellaneous small chapters, based on examples. The goal is to recall and/or introduce useful mathematical tools with hands on.
** Physics and Mathematical Tools: Methods and Examples -- A. Alastuey, M. Clusel, M. Magro, P. Pujol.
** Mathematical Methods for Physicists -- T. L. Chow.
** Group Theory in a Nutshell for Physicists -- Anthony Zee.


* '''Evaluation''' (3 ECTS)
'''Location''': University Paris-Saclay, hbar 625 building, amphi A3/A4/A5, mostly 14:30--16:30,[https://physics-complex-systems.fr/documents.html see website]
** a few exercices during the tutorials
 
** final exam : 3 hours, written exam
'''2021-2022''': Approximate Schedule for the 13 courses:
* 09/09 Functionals derivatives I -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDvariation.pdf tutorial] ('''beware first lecture @11:15''' at the slot of biophysics lecture!!)
<!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDvariation_all.pdf correction] -->
* 09/09 Functionals derivatives II
* 16/09 Complex analysis -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDcomplex.pdf notes & tutorial] -- <!--[http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDcomplexAnalysis.pdf correction]-->
* 23/09 Fourier transform -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDFourier.pdf notes & tutorial]  <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanFourier.pdf correction] -->
* 30/09 Principal value, Kramers-Krönig relations -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDkramers.pdf tutorial] <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDkramers.pdf correction] -->
* 07/10 Gaussian integrals and Wick's theorem [http://lptms.u-psud.fr/membres/groux/enseignements/Math/GaussianAsymptotics.pdf notes & tutorial] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDsteepest.pdf tutorial] <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDgaussiennes.pdf correction] -->
* 21/10 Saddle points methods '''+ 1h test (total 3h)''' => 17:30 <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanLaplaceMethod.pdf Laplace method] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDsteepest.pdf correction] -->
* 25/11 Linear algebra -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDlinearAlgebra.pdf tutorial] <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDLinearAlgebra.pdf correction] -->
* 02/12 Green's function: static case '''(3h)''' => 17:30 -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDGreenFunction.pdf tutorial] <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/ScanTDGreen.pdf correction] -->
* 09/12 Green's function: causality and propagation '''(3h)''' => 17:30 <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanGreen3Dwaves.pdf notes on 3D waves] -->
* 16/12 Orthogonal polynomials and Special functions -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/OrthogonalPolynomials.pdf notes & tutorial] '''(3h)''' => 17:30 <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/RodriguesFormula.pdf Rodrigues formula] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanPolynomials.pdf correction] -->
* Extra: Continuous groups and Lie algebra -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TDgroup.pdf notes & tutorial] <!-- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/groupMorphism.pdf last page] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/scanTDgroup.pdf correction] -->
* Week of 20/01 '''Final Exam (3h)''' 9:00-12:00, on everything
 
'''incomplete bibliography''' :
* [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 '''(free pdf)'''
* [http://www.springer.com/us/book/9783319011943 Mathematical physics: a modern introduction to its foundations] -- S. Hassani
* [http://www.springer.com/gp/book/9780387095035 Mathematical Methods: For Students of Physics and Related Fields] -- S. Hassani
* [http://www.worldscientific.com/worldscibooks/10.1142/9733 Physics and Mathematical Tools: Methods and Examples] -- A. Alastuey, M. Clusel, M. Magro, P. Pujol.
* [https://press.princeton.edu/titles/10773.html 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 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TestComplex2017.pdf Test on complex calculus] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/CorrigeTestComplex2017.pdf correction] (some typos in modulus squares in the correction...)
* 2018--2019 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/TestComplex2018.pdf Test on complex calculus] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/CorrigeTestComplex2018.pdf correction]
<!-- * 2019--2020 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/test_variations2019.pdf Test on variational calculus] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/test_variations2019_corrige.pdf correction] -->
* 2019--2020 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/test_complex2019.pdf Test on complex calculus] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/test_complex2019_corrige.pdf correction]
* 2021--2022 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/test_variations2021.pdf Test on variational and complex calculus] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/test_variations2021_corrige.pdf correction]
 
'''Previous final exams'''
* 2017--2018 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2017.pdf subject] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/corrigeExam2017.pdf correction]
* 2018--2019 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2018.pdf subject] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2018_correction.pdf correction]
* 2019--2020 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2019.pdf subject] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2019_correction.pdf correction]
* 2020--2021 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2020.pdf subject] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2020_correction.pdf correction] (partial correction, too long...)
* 2021--2022 : [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2021.pdf subject] -- [http://lptms.u-psud.fr/membres/groux/enseignements/Math/Exam2021_correction.pdf correction]

Latest revision as of 19:13, 13 February 2022

Bessel function for the drums

Master : an option of the Master 2 Physics of complex system

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.

Location: University Paris-Saclay, hbar 625 building, amphi A3/A4/A5, mostly 14:30--16:30,see website

2021-2022: Approximate Schedule for the 13 courses:

  • 09/09 Functionals derivatives I -- tutorial (beware first lecture @11:15 at the slot of biophysics lecture!!)
  • 09/09 Functionals derivatives II
  • 16/09 Complex analysis -- notes & tutorial --
  • 23/09 Fourier transform -- notes & tutorial
  • 30/09 Principal value, Kramers-Krönig relations -- tutorial
  • 07/10 Gaussian integrals and Wick's theorem notes & tutorial -- tutorial
  • 21/10 Saddle points methods + 1h test (total 3h) => 17:30
  • 25/11 Linear algebra -- tutorial
  • 02/12 Green's function: static case (3h) => 17:30 -- tutorial
  • 09/12 Green's function: causality and propagation (3h) => 17:30
  • 16/12 Orthogonal polynomials and Special functions -- notes & tutorial (3h) => 17:30
  • Extra: Continuous groups and Lie algebra -- notes & tutorial
  • Week of 20/01 Final Exam (3h) 9:00-12:00, on everything

incomplete bibliography :

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

Previous final exams

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