312.104 (21W) Functional Analysis

Wintersemester 2021/22

Registration deadline has expired.

First course session
04.10.2021 08:00 - 10:00 N.2.01 On Campus
... no further dates known

Overview

Due to the COVID-19 pandemic, it may be necessary to make changes to courses and examinations at short notice (e.g. cancellation of attendance-based courses and switching to online examinations).

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

Please note that the currently displayed dates may be subject to change due to COVID-19 measures.
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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.pdf

Examination information

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

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 scheme

Position 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)
  • 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)
  • 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)

Equivalent courses for counting the examination attempts

Wintersemester 2020/21
  • 312.104 VO Functional Analysis (4.0h / 6.0ECTS)
Wintersemester 2019/20
  • 312.104 VO Functional Analysis (4.0h / 6.0ECTS)
Wintersemester 2018/19
  • 312.104 VO Functional Analysis (4.0h / 6.0ECTS)