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
For academic year 2024-2025, the course will be displayed by means of podcast to be followed by the students, which will be followed by a series of proposed exercises. This will allow students to gain understanding of the important concepts in perturbation methods.
Several Q/A sessions will be organized in the late afternoon on appointment for the whole class.
Student will develop a personal project, and discuss this project with the teacher during one-to-one Q/A sessions.
Mode of delivery (face to face, distance learning, hybrid learning)
Remote course
Further information:
For academic year 2024-2025, the course is given remotely.
One-to-one online meetings and group meetings will be organized upon appointement.
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 organized during the 5th week of the semester, on the topics covered in the podcasts.
A personal project will be developed and evaluated through a written report (75%).
Work placement(s)
Organisational remarks and main changes to the course
Contacts
Prof. V. Denoël
v.denoel@uliege.be