Course syllabus

Kontinuerliga system
Applied Mathematics

FMAN55, 7,5 credits, A (Second Cycle)

Valid for: 2021/22
Faculty: Faculty of Engineering, LTH
Decided by: PLED F/Pi
Date of Decision: 2021-04-23

General Information

Main field: Technology.
Compulsory for: F2, Pi2
Elective for: D4, E4, M4
Language of instruction: The course will be given in Swedish


Within the engineering sciences the term "continuous system" means a system whose state space is described by a continuous family of parameters. Continuous systems occur frequently in physics and other natural sciences, in mechanics, electricity and other engineering sciences, in economic sciences, etc. To describe a continuous system one is in general led to partial differential equations (pde).

One aim of the course is to provide mathematical tools, and the ability to use them, for the whole chain model building - analysis - interpretation of solutions to pde:s appearing for such systems. Another aim is the converse: to lay a foundation for a general competence in mathematics, useful in further studies as well as in professional activities, by showing how abstract mathematical concepts, such as Hilbert spaces, may be used in concrete applications. A further aim is that the student should become acquainted with the use and usability of software packages for computation and simulation.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must


Physical models. Fourier's method, series expansions and integral transforms. Green functions. Wave propagation. Function spaces and function norms. Hilbert spaces. Sturm-Liouville operators and their eigenvalues and eigenfunctions, in particular the Laplace operator with simple boundary conditions on simple domains. Special functions, e.g.,  Bessel, Legendre, spherical harmonics. Distributions. The Fourier and Laplace transforms. Something about the numerical solution of partial differential equations.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written test comprising theory and problem solving. Computer sessions. A voluntary test at the middle of the course provides an opportunity to collect credits for the final exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Code: 0117. Name: Applied Mathematics.
Credits: 7,5. Grading scale: TH.
Code: 0217. Name: Laboratory Work.
Credits: 0. Grading scale: UG.


Admission requirements:

Assumed prior knowledge: FMAF01 Analytic Functions and FMAF05 Systems and Transforms.
The number of participants is limited to: No
The course overlaps following course/s: FMAF15, FMA020, FMA022, FMFF15, FMA021

Reading list

Contact and other information

Director of studies: Studierektor Anders Holst,
Course administrator: Studerandeexpeditionen,
Teacher: Mikael Persson Sundqvist,
Course homepage:
Further information: Any credits acquired by passing the voluntary written test at the middle of the course is valid at the examination and at the two resit exams that immediately follow. It is possible to participate in the voluntary test the following year in order to try to acquire new credits. The credits may only be used to raise a failing grade to a pass, but not to raise a pass to a higher mark.