Duration
15h Th, 15h Pr
Number of credits
| Master of Science (MSc) in Engineering Physics | 3 crédits |
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit 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 learning unit
- 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.
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, VI.1, VII.2, VII.4 of the MSc in engineering physics.
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, hybrid learning)
Course in the class, if sanitary conditions allow - See schedule on CELCAT
The courses will be recorded (under technological limits) and uploaded on MyULiege
Recommended or required readings
E.J. Hinch, Perturbation methods, Vol. 1, Cambridge: Cambridge University Press, 1991. S. Howison, Practical Applied Mathematics: Modelling, Analysis, Approximation, Cambridge University Press, 2005.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Written work / report
Out-of-session test(s)
Additional information:
Quizz: 15%
Written exam: 85%
The written exam consists in solving three problems of the familiy of regularly and singularly perturbed problems studied in this course
Work placement(s)
Organisational remarks and main changes to the course
Contacts
Prof. V. Denoël v.denoel@ulg.ac.be