MATH2015-1 : Perturbation methods

Study Programmes 2015-2016

MATH2015-1

Perturbation methods

Duration :

15h Th, 15h Pr

Number of credits :

Master in physical engineering (120 ECTS)		3

Lecturer :

Vincent Denoël

Language(s) of instruction :

English language

Organisation and examination :

Teaching in the second semester

Units courses prerequisite and corequisite :

Prerequisite or corequisite units are presented within each program

Course contents :

The course is divided into four chapters: - Algebraic equations and eigen value problems - Asymptotic Approximations - Matching Asymptotics - Multiple Scales Besdies, some lectures might be adapted to other perturbation-related subjects in order to match the project (e.g. homogenization).

Learning outcomes of the course :

- non-dimensionalization of problems and identification of key parameters - treatment of small parameters in various mathematical problems - development of analytical solutions serving as a validation tool for numerical solvers, or sometimes as the only reasonable solution when numerical solutions become computationally too expensive.

Prerequisite knowledge and skills :

- algebra - calculus (including ODE and an introduction to PDE)

Planned learning activities and teaching methods :

Students are requested to attend the course, taking place during the second semester. The teacher presents theories and methods and illustrates them with examples on the blackborad. Students are invited to train by solving similar problems at home.
A short connection is made with the projet, during the hours of the project.

Mode of delivery (face-to-face ; distance-learning) :