FMAF10F

Temporary

Applied Mathematics - Linear systems

5

Course given jointly for second and third cycle

7151 (Centre of Mathematical Sciences / Mathematics)

2022-11-23

Maria Sandsten

Swedish

Every spring semester

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.

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.

be able to describe different properties of linear systems, and to explain how they can be modelled in the time domain and in the frequency domain.

be able to define the Laplace transform and account for its significance in connection with input/output relations and the solution of differential equations, and be able to use simple transform tables to determine transforms/inverse transforms.

be able to use matrix theory to analyse quadratic forms and to solve systems of linear differential equations.

be able to demonstrate the ability to identify problems that can be modelled with linear systems, and be able to analyse the corresponding models.
be able to demonstrate the abilty to use the introduced concepts in connection with problem solving.
with proper terminology, suitable notation, and with clear logic be able to explain the solution to a problem in a well structured manner.

Lectures

Laboratory exercises

Exercises

Written exam

Failed, pass

linear algebra, calculus

Spanne, S. & Sparr, A.: Föreläsningar i Tillämpad matematik, Lineära system. KFS-Sigma, 1996.
Spanne, S. & Sparr, A.: Övningar i Tillämpad matematik 2, Lineära system.. KFS-Sigma, 1996.

FMAF10F

2022-11-23

Maria Sandsten