312.104 (18W) Functional Analysis
Overview
- Lecturer
- Course title german Functional Analysis
- Type Lecture
- Hours per Week 4.0
- ECTS credits 6.0
- Registrations 11
- Organisational unit
- Language of instruction English
- Course begins on 03.10.2018
- eLearning Go to Moodle course
Time and place
Course Information
Intended learning outcomes
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.
Teaching methodology including the use of eLearning tools
lecture
Course content
- adjoint operators
- reflexivity
- weak convergence
- compact operators
- Fredholm theory
- spectrum
- Riesz theory
- spectral theory in Hilbert spaces
- fixed point theorems
- theory of monotone operators
Prior knowledge expected
It is stroncly recommended to attend the lecture "Einführung in die Funktionalanalysis" before the lecture "Functional Analysis" (not in parallel)
Literature
Christian Clason, University of Duisburg-Essen
Lecture notes on Functional Analysis I
https://www.uni-due.de/~adf040p/skripte/FunktAnSkript15.pdf
Gerald Teschl, University of Vienna
Topics in Real and Functional Analysis
Graduate Studies in Mathematics, Volume XXX, Amer. Math. Soc., Providence, (to appear).
Link to further information
https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdfExamination information
Examination methodology
Oral exam (approx. 30-45 minutes).
Examination topic(s)
contents of the lecture
Assessment criteria / Standards of assessment for examinations
The assessment of the oral exam relies on
- knowledge of the methods, definitions and results;
- good explanation of the correspoding proofs and derivations.
Grading scheme
Grade / Grade grading schemePosition in the curriculum
- Thematic Doctoral Programme Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(SKZ: ---, Version: 16W.1)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
-
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)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Subject: Analysis
(Compulsory subject)
-
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)
-
Subject: Analysis
(Compulsory subject)
- Doctoral programme Doctoral programme in Technical Sciences
(SKZ: 786, Version: 12W.4)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
-
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)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)