2023/24
27035 - Fourier Analysis
Optional
1. General information
This is an elective course within the degree of Mathematics program. Its objective is to introduce the student to the fundamentals of Fourier analysis.
The expression of a periodic function as a Fourier series allows us to study its properties from that of its coefficients. We will analyze the equality function=series with techniques similar to other series expansions learned in the degree. We will study from the functional point of view the Fourier transform and some of its applications (uncertainty principle). Finally, the discretization of the procedures will allow us to use a computer to remove noise or correct drawings, in short, to use filters on signals.
It is necessary to have passed the subjects Mathematical Analysis I, Mathematical Analysis II, Complex Variable and Lebesgue Integral. It is recommended to have passed Functional Analysis. The course requires a good knowledge of the Lebesgue integral and the L1 and L2 spaces.
The approaches and objectives of this module are aligned with the Sustainable Development Goals (SDGs) of the United Nations 2030 Agenda; the learning activities could contribute to some extent to the achievement of the goals 4 (quality education), 5 (gender equality), 8 (decent work and economic growth), and 10 (reducing inequality).
5. Assessment system
As a general rule, the module can be passed either showing a regular work along the academic year, or by a final exam.
- Regular work. During the course, the student results will be evaluated through a periodical supply of exercises or short tasks, together with their active participation during the course. The use of LaTeX in written presentations is recommended; the evaluation can also include oral presentations. These evaluations will constitute 100% of the final mark.
- Final exam. The aforementioned procedure does not exclude the right, according to the current regulations, to a final exam which, by itself, allows to pass the module.