312.104 (19W) Functional Analysis
Überblick
- Lehrende/r
- LV-Titel englisch Functional Analysis
- LV-Art Vorlesung
- Semesterstunde/n 4.0
- ECTS-Anrechnungspunkte 6.0
- Anmeldungen 10
- Organisationseinheit
- Unterrichtssprache Englisch
- LV-Beginn 01.10.2019
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 inkl. Einsatz von eLearning-Tools
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 strongly recommended to attend the lecture "Einführung in die Funktionalanalysis" before the lecture "Functional Analysis" (not in parallel)
Literatur
- R. Kress, Linear Integral Equations. Applied Mathematical Sciences 82, Springer-Verlag, Heidelberg (1989), 2nd Edition (1999), 3rd Edition (2014).
2. G. Teschl, University of Vienna, Topics in Real and Functional Analysis, Graduate Studies in Mathematics, Volume XXX, Amer. Math. Soc., Providence, (to appear).
Link auf weitere Informationen
https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdf
Prüfungsinformationen
Prüfungsmethode/n
Oral exam (approx. 30-45 minutes).
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)