Course Syllabus for

Applied Mathematics - Linear systems
Tillämpad matematik - Linjära system

FMAF10F, 5 credits

Valid from: Spring 2023
Decided by: Maria Sandsten
Date of establishment: 2022-11-23

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMAF10
Teaching language: Swedish


The aim of the course is to treat some mathematical concepts and methods, above the level of calculus in several variables, that are important for further studies within e.g. image analyis, signal processing, control theory, electrical engineering and for further professional activities.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

Linear systems: Mathematical models of linear, time invariant systems. Transfer function. Step response and impulse response. The frequency function. The Laplace transform: Step and impulse functions. Computational rules for the two-sided Laplace transform. Inverse transforms, in particular of rational functions. Use of transform tables. Convolution. Matrix algebra: Eigenvalues and eigenvectors. Diagonalization, in particular of symmetric matrices. Quadratic forms, diagonalization and classification. Systems of differential equations: solution by diagonalization, solution using exponential matrix.

Course Literature

Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises

Examination Details

Examination format: Written exam
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: linear algebra, calculus

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

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