# Fourier Analysis (BM)

Course
2024-2025

Knowledge of linear algebra, elementary topology, real analysis, Lebesgue integration.
It is highly recommended that the students have followed the courses Inleiding Maattheorie and Linear Analysis.
Knowledge of complex analysis is an advantage, but it is not required.

## Description

The course focuses on the theory and applications of Fourier series and the Fourier transform.
In the first part of the course we will introduce classical Fourier theory, focusing on the Fourier series for periodic functions.

In the second part of the course we will describe the Fourier transform on the real line, culminating in
the Fourier transform for test functions and (tempered) distributions. If time allows, we will highlight some applications to other areas of mathematics.

## Course objectives

At the end of the course, the student knows and understands the treated course material and is able to reproduce the content of the course. The student is able to apply the methods of Fourier analysis to concrete problems and understands to problems from different areas of mathematics.

## Timetable

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## Mode of instruction

Lectures: 2 hours per week.
During the course, individual students can hand in a number of assignments (typically 5 or 6), according to a schedule that is provided in Brightspace at the start of the semester.

## Assessment method

During the course, individual students can hand in a number of assignments, according to a schedule that is provided in Blackboard at the start of the semester. The lowest grade for these is stricken, and the homework grade is determined as the (unrounded) average of the remaining grades for these assignments.

The unrounded final grade for the course is the maximum of:
the weighted average of the homework grade (20%),
the maximum of the (unrounded) grades for the written exam and the resit (80%),
the (unrounded) grade for the written exam, and
the (unrounded) grade for the resit.

This maximum is then rounded to the nearest half-integer, but not to 5.5, to obtain the final grade for the course. If the result is 6.0 or higher, this is a "pass", provided that a grade of at least 5.0 (unrounded) has been obtained for the written exam and/or the resit. If the result is 5.0 or lower, or if no grade of at least 5.0 (unrounded) has been obtained for the written exam and/or the resit, this is a "fail".

During the written exam and the resit you can use the textbook of the course and the notes that you may have taken.

Vretblad, Anders. Fourier Analysis and Its Applications. New York: Springer, 2003.

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

• Enrolment for the fall opens in July

• Enrolment for the spring opens in December

Note:

• It is mandatory to enrol for all activities of a course that you are going to follow.

• Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

• Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Both the instructor and the assistants can be reached at the dedicated email address fourieranalysis@math.leidenuniv.nl

## Remarks

Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.