Course syllabus

# Tillämpad matematik - Linjära system

Applied Mathematics - Linear systems

## FMAF10, 5 credits, G2 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

Admission requirements:
## Reading list

## Contact and other information

Applied Mathematics - Linear systems

Valid for: 2023/24

Faculty: Faculty of Engineering, LTH

Decided by: PLED F/Pi

Date of Decision: 2023-04-18

Main field: Technology.

Compulsory for: C3, D2

Elective for: B4, BME4, K4, L4-gi, M4, W4, R4

Language of instruction: The course will be given in Swedish

The aim of the course is to treat some mathematical concepts and methods, above the basic level, that are important for further studies within e.g. machine learning, signal processing, control theory, electrical engineering and for further professional activities.

Knowledge and understanding

For a passing grade the student must

- 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.

Competences and skills

For a passing grade the student must

- 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.

*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.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written test. Computer sessions.

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.

Parts

Code: 0109. Name: Applied Mathematics.

Credits: 5. Grading scale: TH.

Code: 0209. Name: Computer Work.

Credits: 0. Grading scale: UG.

Assumed prior knowledge: Basic university courses in calculus and linear algebra.

The number of participants is limited to: No

The course overlaps following course/s: FMA030, FMA037, FMA062, FMA450, FMAF05

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

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se

Teacher: Victor Ufnarovski, ufn@maths.lth.se

Course administrator: Studerandeexpeditionen, expedition@math.lth.se

Course homepage: https://canvas.education.lu.se/courses/20587