*Note from June 29, 2020*

Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.

5 credits

30.0 h + 22.5 h

Q2

Teacher(s)

Language

French

Prerequisites

*The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.*

Main themes

This course covers themes in mathematical analysis (measure theory, functional analysis and function spaces) that play a role in the foundations of various areas of applied mathematics such as dynamical systems, partial differential equations, optimal control, scientific computing, stochastic processes and financial mathematics.

Aims

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1 |
AA 1.1, 1.2, 1.3, 3.1. |

*The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.*

Content

Important concepts and results within the main themes of the course,

such as:

such as:

- Measure theory, Lebesgue integral, convergence theorems,
- Complete metric spaces, Banach spaces and Hilbert spaces, spaces of continuous functions, spaces of integrable functions,

- Continuous linear mappings, weak convergence, Riesz representation theorem, notions of spectral theory,
- Distributions and Sobolev spaces.

Teaching methods

The course includes interactive lectures and exercises. The emphasis is

on critical understanding of the theory and active problem solving.

on critical understanding of the theory and active problem solving.

Evaluation methods

- Homeworks, exercises, tests or practical work carried out during the semester
- Exam

course outline, made available on Moodle at the beginning of the

academic year.

Other information

Bibliography

Livre de référence : Gerald Teschl, "Topics in Real and Functional Analysis" disponible gratuitement en ligne à l'adresse

(https://www.mat.univie.ac.at/~gerald/ftp/book-fa/).

(https://www.mat.univie.ac.at/~gerald/ftp/book-fa/).

Faculty or entity