Transform Methods
5 credits
Syllabus, Bachelor's level, 1MA034
A revised version of the syllabus is available.
- Code
- 1MA034
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 3 November 2008
- Responsible department
- Department of Mathematics
Entry requirements
Linear Algebra II, Single Variable Calculus or Series and Ordinary Differential Equations
Learning outcomes
In order to pass the course the student should
- be able to give an account of the definitions and properties of the Laplace transform, the z-transform and the Fourier transform;
- be able to use transformation rules to compute transforms, and to use tables to compute inverse transforms;
- be able to compute Fourier coefficients and know some criterion for pointwise convergence of a Fourier series;
- be able to give an account of the concept of a complete ON-system and be familiar with and know how to apply the theorems of Parseval and Plancherel;
- be able to formulate important results and theorems covered by the course;
- be able to use transforms as a technique for solving differential equations and difference equations;
- be able to use transform methods in some area of applications that is characteristic for the education program of the student and to demonstrate this ability by accomplishing a minor project.
Content
The Laplace transform, the z-transform, Fourier series, the Fourier transform. Applications to ordinary and partial differential equations. A project in a selected area of applications, e.g. circuit electronics, spectral analysis, the discrete Fourier transform.
Instruction
Lectures and problem solving sessions. Laboratory work may occur as part of the project.
Assessment
Written examination (4 credit points) at the end of the course. Written project report (1 credit point). Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2022
- Reading list valid from Autumn 2019
- Reading list valid from Spring 2018
- Reading list valid from Spring 2013
- Reading list valid from Autumn 2012, version 2
- Reading list valid from Autumn 2012, version 1
- Reading list valid from Spring 2009, version 2
- Reading list valid from Spring 2009, version 1
- Reading list valid from Spring 2008
- Reading list valid from Autumn 2007, version 2
- Reading list valid from Autumn 2007, version 1