Course Syllabus for

Mathematics - Systems and transforms
Matematik - System och transformer

FMAF05F, 7 credits

Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-10-08

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: FMAF05
Teaching language: Swedish


To make the postgraduate student familiar with several concepts and techniques that are important in modern engineering mathematics.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

● Systems of linear differential equations: Equations in state form. Solution via diagonalization. Stability. Stationary solutions and transients. Solution via exponential matrix. ● Input/output relations: Linearity, time and space invariance, stability, causality. Convolutions. Elementary distribution theory. Transfer and frequency functions. ● Fourier analysis: The Laplace and Fourier transforms. Inversion formulae, the convolution theorem and Plancherel's theorem. Transform theory and analytic functions. Applications to differential equations and systems of differential equations.

Course Literature

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination formats: Written exam, written assignments
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: Linear algebra, calculus in one and several variables. Knowledge about complex analysis is useful for some parts.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

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