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FRTN45 - Mathematical Modelling

FRTN45 Matematisk modellering, fortsättningskurs, 4.5 hp

Syllabus | Schedule | CEQ


Canvas page (2023)


This course focuses on Mathematical Modelling, i.e. the ability to model various phenomena in terms of mathematics. The mathematical models can be used for various purposes; to get increased knowledge about the phenomena, to analyse the phenomena, to simulate the phenomena, to control the phenomena, etc. To construct mathematical models suitable for a defined purpose is a skill. This course will practice these skills. It consists of two lectures, a project (with 100 hours of workload per person), and project presentations.

In 2023, the following dates apply (see Canvas-page for more details and dates for deadline for reviews, project plans, project reports etc.)

  • Lectures
    • Lecture 1: Tuesday January 17 at 13.15-15.00, (MH:Reiszssalen)
    • Lecture 2: Friday January 20 at 13.15-15.00, (MA:3)
  • Feedback seminars (with project plan presentation and review)
    • Tuesday February 6 at 13.15-17.00, (TBA).
  • Project presentations
    • alternative 1: Tuesday February 28 at 13.15-17.00, (TBA).
    • alternative 2: Wednesday March 1 at 13.15-17.00, (TBA)



  • Slides Lecture 1 (see Canvas)
  • Slides Lecture 2 (see Canvas)
  • Each project group will get additional material from supervisors.


  • Yiannis Karayiannidis Course responsible, lecturer (Email:
  • Mika Nishimura Course administrator (Email:
  • Project supervisors listed in Canvas


The project should include the following elements:

  • A Project plan (one A4 page) should be specified together with the supervisor. (See first page of PM on project work.) The plan must be submitted to the course responsible by February 6. Use email with subject line "FRT095".
  • A written report including the items described in section 2.2 of the document Teknisk Rapportskrivning. All three modeling phases (see quote from Ljung and Glad) should be included. The report shall contain the following sections:
    • Title-page.
    • Summary.
    • Table of contents.
    • Main text: 
      • Problem formulation. (What is the purpose of the model?)
      • Summary of used literature.
      • Theory/Method. (Motivate your choices.)
      • Implementation.
      • Results.
      • Evaluation/discussion. (Does the model suit its purpose?)
      • Reference list.
      • Description of how the work is distributed within the group and the supervisor's role.
  • A preliminary version of the report sent by email to the opposition group, the supervisor, and the course responsible at least 2.5 working days before the oral presentation. Final project report, adjusted according to the comments in the report, to be submitted to the course responsible no later than 3 working days after the oral presentation. Use email with subject line "FRTN45".


The oral presenations should take the following in consideration:

  • Oral presentations will be held on two separate occasions during the last week of the course, in the Automatic Control seminar room on the second floor near the south stairs of the M-building. Each group must make a presentation in which all group members are active and all members should be able to answer questions about all aspects of the project. There will an examination board consisting of the supervisors. For each presentation allocated 25 minutes, including 5 minutes reserved for opponent questions.
  • Oral opposition is also shared by all group members. Each group opposes the subsequent group, except for the last group, which gives opposition to the first one.
  • Written opposition report (approximately one page) submitted by email to course responsible before the presentations.


On technical writing, opposition and working in groups

The following documents can be useful for the work:

Reference Literature

Lennart Ljung och Torkel Glad, Modeling and Identification of Dynamic Systems, Studentlitteratur 2016, ISBN 978-91-44-11688-4

Official Course Syllabus

General Information

Compulsory for: Pi3
Elective for: F4, F4-bs, I4
Language of instruction: The course will be given in Swedish


The aim of the course is to stengthen and develop the student's knowledge and skills in modelling in the form of basic theory and a practical project.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

  • have improved his/her basic knowledge about mathematical modelling
  • have developed new knowledge and skills within the area of the project

Competences and skills
For a passing grade the student must

  • be able to perform several of the phases in a typical modelling project: identification of the aim of the model, data collection, analysis, model structure selection, parameter estimation, simulation, validation, documentation, and presentation
  • be able to present the project results on both oral and written form
  • show ability for teamwork and collaboration

Judgement and approach
For a passing grade the student must

  • understand the relations and limitations when simplified models are used to describe a complex reality


The lectures (20% of the course) present different model types and describe the foundations for physical modelling as well as modelling from measured data. Model validation is a central concept. Simulation methods for different model types are presented.

The project part (80% of the course) should involve expertise from several different areas. The project plan and regular project meetings are central parts of the course. The written report should be put in relationship with the content of the lectures.

Examination details

Grading scale: UG - (U,G) - (Fail, Pass)
Assessment: Accepted project. Oral and written project presentation and written and oral opposition.

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.


Assumed prior knowledge: FMAF05 Mathematics - Systems and Transforms, FMSF10 Stationary Stochastic Processes, FMAN55 Applied Mathematics.
The number of participants is limited to: No
The course overlaps following course/s: FRT095

Reading list

  • Lennart Ljung och Torkel Glad, Modellbygge och Simulering, Studentlitteratur, 2nd edition 2004, ISBN 91-44-02443-6.

Contact and other information

Course coordinator: Yiannis Karayiannidis,