Applied Mathematics - Linear systems
Tillämpad matematik - Linjära system

FMAF10F, 5 högskolepoäng

Gäller från och med: Spring 2023
Beslutad av: Maria Sandsten
Datum för fastställande: 2022-11-23

Allmänna uppgifter

Avdelning: Mathematics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMAF10
Undervisningsspråk: Swedish

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• 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.

Kursinnehåll

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.

Kurslitteratur

• 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.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar

Kursens examination

Examinationsform: Skriftlig tentamen
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: linear algebra, calculus

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:
Hemsida: https://canvas.education.lu.se/courses/20587