## Admission requirements

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.

## Mode of instruction

Lectures: 2 hours per week.

During the course, individual students can hand in up to six assignments, 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 (25%),

the maximum of the (unrounded) grades for the written exam and the resit (75%),

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.

## Literature

Vretblad, Anders. Fourier analysis and its applications. Graduate Texts in Mathematics, 223. Springer-Verlag, New York, 2003. xii+269 pp. ISBN: 0-387-00836-5

## Contact

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