Duration
15h Th, 15h Pr
Number of credits
| Master MSc. in Engineering Physics, research focus | 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
This course introduces perturbation methods, a set of techniques used to approximate the solutions of problems that cannot be solved exactly. Perturbation methods are widely applied in various fields such as physics, engineering, and applied mathematics, particularly when dealing with nonlinear systems, differential equations, and complex models.
Learning outcomes of the learning unit
After completion of this course, the student will be able to
- develop non-dimensional versions of problems and identification of key parameters, paying attention to the appropriate choice for small parameters,
- treat small parameters in various mathematical problems, where numerical techniques would typically struggle : algebraic equation, transcendental equation, trigonometric equations, eigenvalue problems, ODEs, PDEs,
- develop approximate analytical solutions serving as a validation tool for numerical solvers, or sometimes as the only reasonable solution when numerical solutions become computationally too expensive,
- formulate solutions of nonlinear problems with the methods of strained coordinates and multiple scales, understand secularity
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
The teaching approach will be structured around a sequential progression of topics, ensuring that each concept builds upon the previous one.
In class, material will be presented step by step, with time dedicated to explanation, examples, and interactive discussion.
To monitor understanding and encourage regular study, a short test will be organized after 2-3 weeks, allowing both students and instructor to verify progress and address potential difficulties early in the course.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Further information:
On campus
Course materials and 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.
Written work / report
Continuous assessment
Out-of-session test(s)
Further information:
A test (25%) is scheduled during the 2nd or 3rd week of the semester.
A written exam (75%) focuses on solving 3 or 4 problems similar to those covered in the course.
Work placement(s)
Organisational remarks and main changes to the course
Contacts
Prof. V. Denoël
v.denoel@uliege.be