Modelisation and scientific computing - 3EU5MCS6

Informations générales

  • Number of hours

    • Lectures 36.0
    • Projects -
    • Tutorials 38.0
    • Internship -
    • Laboratory works 22.0

    ECTS

    ECTS 7.5

Goal(s)

Understand the concept of spectral representation of a signal and master the associated mathematical framework. Identify typical situations in engineering science where this representation is essential. Characterization of time invariant systems as convolution operators, spectral and temporal study of these operators.

Understand the fundamental results related to the most commonly used equations for modeling physical phenomena (ODEs, PDEs). Understand how to perform explicit solutions when possible (linear ODEs, methods of characteristics for the transport equation, separation of variables method for the diffusion or wave equation). Qualitative studies of EDOs around equilibrium points : stability and phase portraits. Geometrical and physical understanding of most commonly used differential operators (gradient, divergence, laplacian, curl).
Understand the fundamental concepts of a scientific computing algorithm (consistency, stability, convergence, explicit/implicit numerical scheme). Master the finite difference method to numerically solve ODEs or PDEs with 1D evolution. Implement these algorithms in Python.

Responsible(s)

Hugues BODIGUEL, Antoine VEZIER

Content(s)

• Harmonic analysis : Lebesgue integral, Hilbert space, Fourier series, Fourier and Laplace transforms
• Differential geometry : differential calculus in euclidean space, qualitative of vector fields and EDOs, classification of linear dynamics in the plane. Transport and diffusion EDP.
• Scientific Computing: Finite Difference Method for ODEs and PDEs, Newton's Method, Jacobi/Gauss-Seidel/SOR Method.

Prerequisites

L2 Level Mathematics: https://membres-ljk.imag.fr/Bernard.Ycart/mel
The basics of the Python language.

Test

Session 1

ET1 : 1 halfway exam of 1h30 Fourier analysis (no documents/calculator).
1 final exam of 2h on differential calculus, scientific computing and physics (no documents/calculator).

Session 2

ET2 : 1 exam of 3h on all the course (no documents/calculator).

Calendar

The course exists in the following branches:

  • Curriculum - Year 1 Engineering Bachelor Degree - Semester 5
see the course schedule for 2026-2027

Additional Information

Course ID : 3EU5MCS6
Course language(s): FR

You can find this course among all other courses.

Bibliography

Cours de calcul différentiel, Henri Cartan.
Méthodes mathématiques pour les sciences physiques, Laurent Schwartz