312.104 (21W) Functional Analysis
Überblick
Weitere Informationen zum Lehrbetrieb vor Ort finden Sie unter: https://www.aau.at/corona.
- Lehrende/r
- LV-Titel englisch Functional Analysis
- LV-Art Vorlesung
- LV-Modell Präsenzlehrveranstaltung
- Semesterstunde/n 4.0
- ECTS-Anrechnungspunkte 6.0
- Anmeldungen 13
- Organisationseinheit
- Unterrichtssprache Englisch
- LV-Beginn 04.10.2021
- eLearning zum Moodle-Kurs
Zeit und Ort
LV-Beschreibung
Intendierte Lernergebnisse
After successful completion of this course, students will know methods and corresponding theoretical results on functional analysis. They will understand and will be able to prove these theorems and will be able to apply these methods.
Lehrmethodik
lecture
Inhalt/e
- adjoint operators
- reflexivity
- weak convergence
- compact operators
- Fredholm theory
- spectrum
- Riesz theory
- spectral theory in Hilbert spaces
- fixed point theorems
- theory of monotone operators
Erwartete Vorkenntnisse
It is stroncly recommended to attend the lecture "Einführung in die Funktionalanalysis" before the lecture "Functional Analysis" (not in parallel)
Literatur
Christian Clason, University of Graz
Introduction to Functional Analysis,
Compact Textbooks in Mathematics, Springer, 2020
Lecture notes on Functional Analysis (in German)
https://www.uni-due.de/~adf040p/skripte/FunktAnSkript15.pdf
Gerald Teschl, University of Vienna
Topics in Real and Functional Analysis
Graduate Studies in Mathematics, Amer. Math. Soc., Providence, to appear.
Link auf weitere Informationen
https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdfPrüfungsinformationen
Prüfungsmethode/n
Oral exam (approx. 30-45 minutes).
The first offered exam date is Friday, January 28.
Other than this, you can make an individual appointment for your exam (please just write me an email approximately 3 weeks before the intended date).
Prüfungsinhalt/e
contents of the lecture
Beurteilungskriterien/-maßstäbe
The assessment of the oral exam relies on
- knowledge of the methods, definitions and results;
- good explanation of the correspoding proofs and derivations.
Beurteilungsschema
Note BenotungsschemaPosition im Curriculum
- Doktoratsprogramm Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(SKZ: ---, Version: 16W.1)
-
Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Pflichtfach)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
- 312.104 Functional Analysis (4.0h VO / 6.0 ECTS)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Pflichtfach)
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Fach: Analysis
(Pflichtfach)
-
1.1 Functional Analysis (
4.0h VO / 6.0 ECTS)
- 312.104 Functional Analysis (4.0h VO / 6.0 ECTS)
-
1.1 Functional Analysis (
4.0h VO / 6.0 ECTS)
-
Fach: Analysis
(Pflichtfach)
- Doktoratsstudium Doktoratsstudium der Technischen Wissenschaften
(SKZ: 786, Version: 12W.4)
-
Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Pflichtfach)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
- 312.104 Functional Analysis (4.0h VO / 6.0 ECTS)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Pflichtfach)