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 both ex-cathedra lectures and exercise sessions.
Mode of delivery (face-to-face ; distance-learning)
Face-to-face
Recommended or required readings
The slides used during the lectures are available on
http://www.montefiore.ulg.ac.be/~geuzaine/MATH0504/
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)
Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session
Teaching methods implemented : distance-learning
Assessment subjects
Assessment methods
Contacts
Adaptation of teaching commitments following the COVID-19 pandemic for the Aug-Sept 2020 session
Assessment subjects
The exam covers the content of all the theoretical lectures and exercise sessions organized during the fall semester.
Assessment methods
Written online exam, with video-surveillance (LifeSize software).
The exam will be open book, with both theorical reflection questions and exercices.
Using electronic tools will be forbidden during the exam, with the exception of those tools necessary to access the video-surveillance.
After the exam the students will need to upload a PDF copy of their answers on an online platform (eCampus).
The detailed procedures to access the video-surveillance and the online platform will be communicated in due time.
Contacts
Benjamin Dewals (b.dewals@uliege.be, 04 366 92 83)
Christophe Geuzaine (cgeuzaine@uliege.be, 04 366 37 30)