TrainingsMasterMathématiques et applicationsCoursesHilbert and Fourier analysis

Master Mathématiques et applicationsUE Hilbert and Fourier analysis

Content

The purpose of this course is to revise and deepen the fundamental concepts of Fourier and Hilbert analysis and to illustrate the different notions through applications in biology. The following concepts will be investigated :

  • Fourier series
    • The classical theorems Dirichlet, Fejer, Plancherel Parseval
    • Regularity and decrease of Fourier coefficients
    • Fast Fourier Transform
    • Application to the representation of biological signals in neuroscience
  • Fourier Transform
    • Reminders of the main results
    • Applications to elliptic equations in unbounded domain arising in biology
  • Hilbert spaces
    • Hilbertian bases, examples
    • Galerkin approximation
    • Application to elliptic equations in bounded domain arising in biology

Language used

Main language used by this course: Anglais.

Fundamental prerequisites

  • Continuous dynamical systems,
  • Linear algebra
  • Modelling
  • Functional analysis

Structure and organisation

Lectures will provide a summary of basic concepts, which will be applied in practicals.

Volume of teachings

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

The trainings which use this course