Course - Fourier Analysis - TMA4170
TMA4170 - Fourier Analysis
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | C |
Course content
The course is intended to give the students a thorough introduction to Fourier analysis. Topics that are covered are: Fourier series and Fourier integrals; pointwise, uniform, and mean convergence of Fourier series; approximation kernels; Parseval's identity and Bessel's inequality; Plancherel's identity; the Schwartz space, convolutions, the Poisson summation formula, Heisenberg's uncertainty principle, selected applications in mathematics (for example partial differential equations and number theory) and in technology (for example signal processing). Topics that may be included in the course: Fourier transforms of distributions, discrete Fourier transforms, Fast Fourier Transform, filter theory, wavelets.
Learning outcome
1. Knowledge. The student has a knowledge of concepts and methods from Fourier analysis, as specified under "academic content". 2. Skills. The student is able to apply his or her knowledge of Fourier analysis to solve mathematical and technological problems.
Learning methods and activities
Lectures and exercises. Retake of examination may be given as an oral examination. The lectures may be given in English. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments.
Further on evaluation
see «Teaching methods and activities».
Recommended previous knowledge
The course is based on TMA4100/05/10/15/20 Calculus 1/2/3/4K, or equivalent. It is an advantage to have TMA4145 Linear Methods. For students who have their background from Mathematical sciences: MA1101 Calculus I, MA1201 Linear Algebra and Geometry.
Course materials
Will be announced at the start of the course.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| SIF5027 | 7.5 |
Version: 1
Credits:
7.5 SP
Study level: Second degree level
Term no.: 1
Teaching semester: SPRING 2024
Language of instruction: English, Norwegian
Location: Trondheim
- Mathematics
- Technological subjects
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 100/100 C INSPERA
-
Room Building Number of candidates - Summer UTS School exam 100/100 C INSPERA
-
Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"