Approximations : methods et theory

Teacher(s)

Claeys Tom;

Language

French

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.

Online resources

https://moodleucl.uclouvain.be/course/view.php?id=12858

Faculty or entity

MATH