MATH0504-1

Duration

26h Th, 26h Pr

Number of credits

	Bachelor in engineering	5 crédits

Lecturer

Benjamin Dewals, Christophe Geuzaine

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The course introduces partial differential equations(PDE) and completes the teachings of matrix algebra
1. Introduction to partial differential equations:

Classification of different PDE types (order, linearity, ellipticity, characteristics, initial and boundary conditions)
Solution types of fundamental PDEs and link with physics (problems of convection, waves, diffusion, elliptic problems; notion of strong and weak solution)
Simple numerical methods (finite difference and finite elements in 1D)

2. Complements of linear algebra:

Subspace methods (conjugate gradient; link between solving linear systems and optimization; application to a linear system obtained from the introduction to PDEs);
Singular value decomposition (SVD) (theory; link with eigenvalue problems; algorithmics);
Applications of SVD (analysis of large data sets; low-rank approximation; matrix conditioning).

Learning outcomes of the learning unit

At the end of the course, the student will be able to:

Understand the fundamental properties of order 1 and order 2 PDEs;
Determine adequate initial and/or boundary conditions for each PDE type;
Solve simple PDEs analytically and numerically;
Understand fundamental physical phenomena and modeling hypothesis (problems of convection, waves, diffusion, elliptic problems);
Understand fundamental principles of iterative subspace methods;
Master the singular value decomposition and understand its application to practical problems.

Prerequisite knowledge and skills

MATH502-1 (Analyse mathématique 2) and MATH0006-3 (Introduction to numerical analysis)

Planned learning activities and teaching methods

The course includes both ex-cathedra lectures and mandatory exercise sessions.

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

Face-to-face

Assessment methods and criteria

Written exam in January and September.

Work placement(s)

Organizational remarks

Lectures given during the first quadrimester (Q1)

Contacts

Benjamin Dewals (b.dewals@uliege.be)
Christophe Geuzaine (cgeuzaine@uliege.be)

Applied mathematics