Approximations : methods et theory

lmat1351  2022-2023  Louvain-la-Neuve

Approximations : methods et theory
5.00 credits
30.0 h + 30.0 h
Q1
Teacher(s)
Claeys Tom;
Language
Prerequisites
Basic numerical analysis courses (e.g., LMAT1151 or LFSAB1104), basic concepts of linear algebra and analysis.
Main themes
- Interpolation
  • polynomial interpolation,
  • piecewise approximations and splines.
- Fourier analysis
  • Fourier coefficients,
  • Fourier series,
  • convergence and Gibbs phenomenon,
  • Fejer process.
- Numerical integration
  • basic methods,
  • quadrature rules.
Evaluation will be based on an exam and projects.
Learning outcomes

At the end of this learning unit, the student is able to :

1 At the end of this activity, the student will be able to :
- implement approximation methods using software,
- construct, mathematically analyze and evaluate approximation methods.
 
Content
Topics covered :
- Introduction to approximation theory
- Approximation by polynomials
- Approximation by trigonometric polynomials
- Polynomial interpolation
- Introduction to Bézier curves and splines
- Fourier series
- Orthogonal polynomials,
- Quadrature rules.
At the end of this activity, the student will be able to :
- implement approximation methods using software,
- construct, mathematically analyze and evaluate approximation methods.
Teaching methods
Lectures and practice sessions
Evaluation methods
The evaluation will consist of an exam, which will contain more theoretical questions and exercises, and a project to be done during the quadrennium. Students registered for the September term may choose to submit a revised version of the project.
Faculty or entity
MATH


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Bachelor in Mathematics