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# Details for Course FMAF05F Mathematics - Systems and transforms

General
• FMAF05F
• Temporary
Course Name
• Mathematics - Systems and transforms
Course Extent
• 7
Type of Instruction
• Course given jointly for second and third cycle
• 7151 (Centre of Mathematical Sciences / Mathematics)
• 2018-10-08
• Professor Thomas Johansson

## Current Established Course Syllabus

General
Aim
• To make the postgraduate student familiar with several concepts and techniques that are important in modern engineering mathematics.
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.
Knowledge and Understanding
• For a passing grade the doctoral student must
• be familiar with the significance of eigenvalues in the context of stability and resonance, in linear systems, with continuous as well as discrete time.

be able to describe and use the concepts of linearity, time invariance, stability, causality, impulse response and transfer function.

be able to describe the structure of an exponential matrix, and be able to compute exponential matrices in simple cases.

be able to define the concept of convolution, continuous and discrete, and to use convolutions both in the context of linear, time invariant systems and in the description of certain types of integral equations.
Competences and Skills
• For a passing grade the doctoral student must
• be able to demonstrate an ability to independently choose appropriate methods to solve systems of linear differential and difference equations, and to carry out the solution essentially correctly.

be able to demonstrate an ability to use eigenvalue techniques, elementary distribution theory, function theory, Fourier and Laplace transforms and convolutions in problem solving within the theory of linear systems.

in connection with problem solving, be able to demonstrate an ability to integrate knowledge from the different parts of the course.

with proper terminology, in a well-structured manner and with clear logic be able to explain the solution to mathematical problems within the framework of the course.
Judgement and Approach
• For a passing grade the doctoral student must
Types of Instruction
• Lectures
• Exercises
Examination Formats
• Written exam
• Written assignments
• Failed, pass
Assumed Prior Knowledge
• Linear algebra, calculus in one and several variables. Knowledge about complex analysis is useful for some parts.
Selection Criteria
Literature
• math-ssp: Lineära system.. KF-Sigma, 1997.
math-ssp: Övningar i Lineära system.. KF-Sigma, 2009.
Further Information
Course code
• FMAF05F
• 2018-10-08
• Professor Thomas Johansson

## All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Autumn 2018 2018‑10‑05 08:32:23 2018‑10‑05 11:43:37 2018‑10‑08

## Current or Upcoming Published Course Occasion

No matching course occasion was found.

## All Published Course Occasions

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