Course syllabus

Mathematics - Systems and Transforms
Matematik - System och transformer

FMAF05, 7.0 credits, G2 (First Cycle)

Valid for: 2024/25
Faculty: Faculty of Engineering LTH
Decided by: PLED F/Pi
Date of Decision: 2024-04-15
Effective: 2024-05-08

General Information

Main field: Technology Depth of study relative to the degree requirements: First cycle, in-depth level of the course cannot be classified
Mandatory for: E2, F2, I2, Pi2
Elective mandatory for: D2
Elective for: BME4, C4, M4, N3
Language of instruction: The course will be given in Swedish

Aim

The aim of the course is to present mathematical concepts and methods from linear algebra and analysis which are important in systems theory (continuous and discrete), and for further studies within e.g. mathematics, economy, physics, mathematical statistics, mechanics, control theory, signal theory and for future professional work. The aim is also to develop the student's ability to solve problems, to assimilate mathematical text and to communicate mathematics.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must

Judgement and approach
For a passing grade the student must

Contents

Linear algebra: Spectral theory, quadratic forms.

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. Discrete systems.

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.

Examination details

Grading scale: TH - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment: Written test comprising theory and problems. Assignments, requiring work with and without computer, which have to be completed BEFORE the exam.

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.

Modules
Code: 0116. Name: Systems and Transforms.
Credits: 7.0. Grading scale: TH - (U, 3, 4, 5). Assessment: Written exam comprising theory and problems.
Code: 0216. Name: Assignments.
Credits: 0.0. Grading scale: UG - (U, G). Assessment: Problems during the course on subjects that have been introduced recently. The aim is to help the student discover if they have missed or misunderstood central concepts.

Admission

Admission requirements:

Assumed prior knowledge: FMAF01 Analytic functions.
The number of participants is limited to: No
Kursen överlappar följande kurser: FMA030 FMA036 FMA062 FMA450 FMAF10

Reading list

Contact and other information

Course coordinator: Studierektor Anders Holst, Studierektor@math.lth.se
Course administrator: Studerandeexpeditionen, expedition@math.lth.se
Course homepage: https://canvas.education.lu.se/courses/20449
Further information: In order for an exam to be graded it is necessary that the examinee has passed on the assignments before the exam.