Mathematical analysis : complements

linma1315  2021-2022  Louvain-la-Neuve

Mathematical analysis : complements
5.00 credits
30.0 h + 22.5 h
Q2
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 :

1 AA 1.1, 1.2, 1.3, 3.1.
At the end of the course, the student will be able to:
1. by means of examples, statements and mathematical proofs, describe infinite-dimensional spaces, including their operators and convergence notions, and compare them to finite dimensional spaces,
2. apply definitions and results of measure theory to the study of function spaces and probability theory,
3. use advanced concepts of measure theory and functional analysis in applied mathematics.
 
Content
Important concepts and results within the main themes of the course,
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.
Evaluation methods
  • Homeworks, exercises, tests or practical work carried out during the semester
  • Exam
More elaborate information on the evaluation procedure is given in the
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/).
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Minor in Applied Mathematics

Specialization track in Applied Mathematics