101.957 Seminar with seminar paper on Numerical Analysis: Fixed point theorems
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2022S, SE, 2.0h, 3.0EC
TUWEL

Properties

  • Semester hours: 2.0
  • Credits: 3.0
  • Type: SE Seminar
  • Format: Presence

Learning outcomes

After successful completion of the course, students are able to to give well understandable, correct and clear lectures with content from mathematics or other nature sciences and to write a survey about the given talk.

Subject of course

This term, we focus on fixed point theorems and applications. In many proofs, fixed point arguments are the main arguments. For instance, the Banach fixed point theorem is used to prove the theorem on implicit functions (Analysis 2), the theorem of Picard-Lindelöf (ordinary differential equations), or the Jacobi iteration for the iterative solution of linear systems (Numerical Mathematics).

In this seminar, we are going to discuss the fixed point theorems of Banach, Brouwer, and Schauder. One main concern is on the respective assumptions of these theorems. We will also study counter examples if the assumptions are relaxed. Dependent on the knowledge and interests of the participants, possible applications of fixed point arguments are taken from the analysis and numerics of ordinary or partial differential equations.

If you want to participate and to give a lecture, please contact Dirk Praetorius via email dirk.praetorius@tuwien.ac.at to make an appointment and to fix the topic of a possible talk.

Teaching methods

Personally support of the student

Mode of examination

Immanent

Additional information

While I have reserved a lecture hall for Thursday 12:00 - 14:00. The seminar talks will start in April.

Please consider the plagiarism guidelines of TU Wien when writing your seminar paper: Directive concerning the handling of plagiarism (PDF)

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Tue12:00 - 14:0028.06.2022Sem.R. DA grün 04 Seminar mit Seminararbeit aus Numerik: Fixpunktsätze

Examination modalities

Satisfying lecture and satisfying written seminar report

Course registration

Not necessary

Curricula

Study CodeSemesterPrecon.Info
033 201 Technical Mathematics 5. SemesterSTEOP
Course requires the completion of the introductory and orientation phase

Literature

No lecture notes are available.

Language

if required in English