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## Fourier Analysis

2019-2020

### Course Objective

At the end of this course the student is able to:
a) Calculate the Fourier series of a given Riemann-integrable function
b) Determine the pointwise and prove the mean-square convergence of a
Fourier series
c) Determine good kernels
d) Apply Fourier series theory to Cesàro and Abel summability
e) Calculate the Fourier transfom on the real line
f) Apply the Fourier transform to some PDE's

### Course Content

Topics that will treated are:
a) The genesis of Fourier Analysis, in particular the investigation of
the wave equation
b) Basic Properties of Fourier Series (uniqueness, convolutions,
Dirichlet and Poisson kernels)
c) Convergence of Fourier Series (pointwise, mean-square)
d) Cesàro and Abel Summability
e) Some applications of Fourier Series
f) The Fourier transform on the real line (definition, inversion,
Plancherel formula)
g) Applications of the Fourier transform to some partial differential
equations

### Teaching Methods

Lectures (1x2 hours per week) and Tutorials (1x2 hours per week).
Active participation during the tutorials is expected!

### Method of Assessment

There are hand-in exercises with grade H, a midterm with grade M and a
final exam with grade F. Let A=.5(M+F) and B=.1 H+.9 A. To pass the
course the student must have A>=.5 and B>=5.5. The final grade is then
B. There is one resit opportunity for the full course. The grade for the
homework does not count toward the grade of resit.

### Literature

Mandatory literature:

Fourier Analysis, an Introduction, by Elias M. Stein and Rami Shakarchi.
Princeton Lectures in Analysis I. Princeton University Press, 2003,
ISBN-13: 978-0691113845.

### Target Audience

Bachelor Mathematics Year 2

### Recommended background knowledge

First year courses Single variable calculus, Multivariable calculus,
Linear algebra, and Mathematical analysis.

### General Information

Course Code XB_0005 6 EC P1+2 200 English Faculty of Science dr. T.O. Rot prof. dr. G.J.B. van den Berg dr. T.O. Rot

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

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