Duration
30h Th, 20h Pr, 25h Proj.
Number of credits
| Master of Science (MSc) in Biomedical Engineering | 5 crédits | |||
| Master of Science (MSc) in Engineering Physics | 4 crédits |
Lecturer
Language(s) of instruction
English 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
This course offers an introduction to modeling using PDEs.
1. Classification of PDEs.
Equilibrium:
2. Theory of distributions.
3. Laplace/Poisson equation.
4. Weak formulation, Galerkin projection, and finite element method.
5. Abstract formulation. Error analysis. Spectral problem.
Evolution:
6. Heat equation. Linear transport equation. Wave equation.
7. Time integration. Method of lines. Semi-discrete problem. Fully discrete problem.
8. Diagonalisation. Von Neumann. CFL. Dissipation and dispersion errors.
Nonlinear:
9. Nonlinear conservation laws. Nonlinear waves.
Learning outcomes of the learning unit
This course offers an understanding of the physical basis, mathematical structure, and numerical solution of different types of PDE, as well as of the relationships between these physical, mathematical, and computational perspectives.
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.3, IV.1, IV.2, VI.1, VI.2, VI.3, VII.2, VII.4 of the MSc in biomedical engineering.
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.2, III.3, III.3, IV.1, IV.2, VI.1, VI.2, VI.3, VII.2, VII.4 of the MSc in engineering physics.
Prerequisite knowledge and skills
This course assumes that students have a background in calculus (real and vector calculus, trigonometry, ordinary differential equations, Fourier analysis), linear algebra, mechanics and physics, and the use of scientific software (such as Matlab or Python). The required background material will be recalled in class as needed.
Planned learning activities and teaching methods
The course takes the form of a series of lectures. The lectures are complemented by discussion sessions and homeworks, which revolve around reading assignments, analytical exercises, numerical exercises, and combinations thereof.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face.
Recommended or required readings
Each lecture is supported by slides prepared by the instructor. The slides are complemented by relevant chapters from selected books, which the university library provides online access to. For students wishing to consult additional material, comprehensive reference texts are recommended during the first lecture.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions ) AND oral exam
Written work / report
Additional information:
The assessment is based on regular homework and a final exam. The final grade is a weighted average of the grades obtained for the regular homework (1/3) and for the final exam (2/3).
The regular homework must be turned in at several due dates in the first semester, and it is not possible to submit an updated version of the work for regrading in the September exam session. The final exam takes place in the January exam session, and it is possible to retake the final exam in the September exam session. Participation to all discussion sessions is mandatory.
Work placement(s)
Organisational remarks and main changes to the course
The course is offered in the Fall semester.
Contacts
Maarten Arnst
Office: B52 - 0/419
Email: maarten.arnst@uliege.be