MATS315 Fourier Analysis (4–9 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028
Description
Fourier series, Fourier transform, Fourier analysis in different function classes, applications.
Learning outcomes
- the student knows basic properties of Fourier series
- the student knows the definition and properties of the Fourier transforms
- the student is familiar with Fourier analysis in different function classes
- the student is aware of applications of Fourier analysis
Additional information
Lectured biennially. The course is tentatively planned to be taught in the fall semesters of 2024 and 2026.
Description of prerequisites
Measure and integration 1. Measure and integration 2 is also recommended (the course employs L^p spaces and Hölder inequality). Additionally students are expected to be familiar with basic computations for complex numbers and with the notation e^{it}.
Study materials
Lecture notes.
Additional reading:
- Stein, Shakarchi: Fourier analysis: an introduction. Princeton University Press, 2003.
- Grafakos: Classical Fourier analysis. Third edition, Springer, 2014.
Completion methods
Method 1
Evaluation criteria:
A sufficient amount of points from exercises and/or seminar presentation and/or exam, depending on the implementation of the course.
Select all marked parts
Method 2
Evaluation criteria:
The grade is decided by the performance in the exam.
Select all marked parts
Parts of the completion methods
x
Teaching (4–9 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
Finnish
Teaching
9/5–10/27/2024 Lectures
x
Exam (4–9 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
The grade is decided by the performance in the exam.
Language:
English, Finnish