Course syllabus


FMFN05, 7,5 credits, A (Second Cycle)

Valid for: 2023/24
Faculty: Faculty of Engineering, LTH
Decided by: PLED F/Pi
Date of Decision: 2023-04-18

General Information

Language of instruction: The course will be given in English on demand


The aim of the course is to introduce chaotic systems and different approaches towards non-linear problems. Several conceptual tools and examples to approach and interpret the non-linear are provided to the student in order to understand complex systems and their eventually chaotic nature. The course shows the pervasive nature of these concepts and gives a possibility to reflect over the fascinating phenomena which may show up in chaotic systems. The abstract and theoretical nature of chaos theory is declined in practical and concrete concepts. For example, strange attractors will highlight the importance of fractal geometry, in order to discuss the posibility that the Solar system is unstable over a longer time scale. The fascinating universality of chaotic behaviour across science and technology will deliver a precious lesson on the beauty and impact of mathematical investigation of phenomena.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must

Judgement and approach
For a passing grade the student must



The course gives an introduction to non-linear and chaotic systems, i.e. non-linear systems that are deterministic but with a time development which is not predictable over longer periods. The study of non-linear systems is an application of mathematics with profound impact on our understanding of physical, biological, computer, and complex systems in general. The course will introduce the mathematical methods needed to study discrete and continuous non-linear systems. Then, it will provide examples of non-linear systems in science and technology.

Temporally discrete systems

Continuous systems

After the basic discrete and continuous representations, students must choose an additional study module. Different study modules can be offered according to need and availability, including the application of chaos theory in physics, or biology, economics. One of this study modules is always offered.

Conservative systems and the KAM theory


Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Examination takes place through a written examination at the end of the course, and the written report of the group project.

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: 0109. Name: Chaos.
Credits: 6. Grading scale: TH. Assessment: Written exam. Contents: The theoretical part of the course.
Code: 0209. Name: Project.
Credits: 1,5. Grading scale: UG. Assessment: Presentaion of project. Contents: Project


Assumed prior knowledge: Elementary mathematics and mechanics.
The number of participants is limited to: No
The course overlaps following course/s: FMF090, FMF092

Reading list

Contact and other information

Course coordinator: Andrea Idini,
Course homepage: