Teacher(s)
Language
French
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.
Learning outcomes
At the end of this learning unit, the student is able to : | |
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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,
- Other topics related to the course themes.
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
- Activities carried out during the term: homework assignments, classroom exercises, project reports, presentations, supervision meetings with the teachers or TAs during office hours, or laboratory work. These activities are thus organized (and evaluated) only once per academic year. The activities will be announced via the News forum on Moodle.
- Exam: written, or oral depending on the circumstances.
Other information
Online resources
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
