Duration
26h Th, 26h Pr
Number of credits
| Bachelor of Science (BSc) in Engineering | 5 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
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)
- 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 theory lectures and exercise sessions.
Mode of delivery (face to face, distance learning, hybrid learning)
Blended learning
Additional information:
Face-to-face, hybrid or online depending on sanitary rules.
Recommended or required readings
The theory slides, the exercise manual and the exams from previous years are available on the course website.
Exam(s) in session
Any session
- In-person
written exam
Additional information:
Written exam in January and September.
Work placement(s)
Organisational remarks and main changes to the course
Lectures given during the first quadrimester (Q1)
Main changes: The organization of some classes will be slightly adjusted to take full advantage of the time available. Particular care will be taken to prepare and monitor the organization of practical sessions.
Contacts
Benjamin Dewals (b.dewals@uliege.be)
Christophe Geuzaine (cgeuzaine@uliege.be)
Association of one or more MOOCs
https://explore.lib.uliege.be/permalink/32ULG_INST/1iujq0/alma9919527387602321