312.104 (21W) Functional Analysis
Overview
For further information regarding teaching on campus, please visit: https://www.aau.at/en/corona.
- Lecturer
- Course title german Functional Analysis
- Type Lecture
- Course model Attendance-based course
- Hours per Week 4.0
- ECTS credits 6.0
- Registrations 13
- Organisational unit
- Language of instruction English
- Course begins on 04.10.2021
- 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
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 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 to further information
https://www.mat.univie.ac.at/~gerald/ftp/book-fa/fa.pdfExamination information
Examination methodology
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).
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)