Applied Mathematical Modelling and Analysis (PET933)
The course introduces methods for deriving and analyzing mathematical models of systems and processes within science and engineering. The course focuses on the development of approximate solutions to problems in physics and engineering by the use of dimensional analysis, scaling and perturbation methods.
Course description for study year 2025-2026. Please note that changes may occur.
Course code
PET933
Version
1
Credits (ECTS)
10
Semester tution start
Autumn
Number of semesters
1
Exam semester
Autumn
Language of instruction
English
Content
The main contents of the course are:
- Dimensional analysis and the Pi-theorem
- Non-dimensionalization and scaling
- Regular and singular perturbation theory
- Fixed points, stability and bifurcations in nonlinear dynamical systems
- Derivation and analysis of partial differential equations from conservation principles
The course will focus on the development and analysis of mathematical models, as well on how these models can be used to motivate, design and interpret experiments. Throughout the course, example problems from classical mechanics and/or fluid mechanics will be used to illustrate the application of both analytical and numerical methods. Examples may include mechanical vibrations of slender structures, population (predator-prey) models, advection and diffusion processes, or general viscous flows in two-dimensional geometries.
Learning outcome
Upon successful completion of the course, the student will be able to:
- Apply conservation principles to derive mathematical models of a wide range of physical systems and processes,
- Use dimensional analysis and scaling to analyze and simplify models,
- Solve mathematical models using regular and singular perturbation techniques, as well as numerical methods,
- Actively use mathematical models to design experiments and analyze measurements.
Required prerequisite knowledge
Recommended prerequisites
Exam
Oral exam and project assignment
| Form of assessment | Weight | Duration | Marks | Aid |
|---|---|---|---|---|
| Oral exam | 2/5 | Passed / Not Passed | ||
| Project assignment | 3/5 | Passed / Not Passed | None permitted |
Course assessment: Project report and oral project presentation (60%), followed by oral examination based on the course curriculum (40%). The oral project presentation may adjust the initial evaluation of the written project report.All parts of the assessment must be passed in order to get a final grade in the course.No re-take or continuation will be granted for the course report. Candidates that do not pass the regular assessment of the report, may instead make a new report the next time the course is offered.