312.190 (19W) Seminar in Analysis

Wintersemester 2019/20

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04.10.2019 23:59

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Überblick

Lehrende/r
LV-Titel englisch
Seminar in Analysis
LV-Art
Seminar (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechungspunkte
4.0
Anmeldungen
2 (15 max.)
Organisationseinheit
Unterrichtssprache
Englisch
mögliche Sprache/n der Leistungserbringung
Englisch
LV-Beginn

LV-Beschreibung

Intendierte Lernergebnisse

Preparation for a theses and further research in the field of Dynamical System

Lehrmethodik

Talks based on the references below

Inhalt/e

Numerical dynamics is a field in the intersection between Dynamical Systems and Numerical Analysis. The central questions are as follows:

  • Which properties of a dynamical system (attractors, invariant manifolds, boundedness) given by an ordinary differential equation persist under discretization using one- or multistep methods (persistence)?
  • Do the discretized objects converge to the original ones preserving the convergence rate of the method (convergence)?
  • Which observations obtained from a discretization or simulation allow to draw conclusions to the original equation (shadowing)?

Preliminary talks (Vorbesprechung): August 01, 10:00, N.2.15

Erwartete Vorkenntnisse

Dynamical Systems, Numerical Analysis of ODEs

Literatur

[0] A.M. Stuart and A.R. Humphries, Dynamical systems and numerical analysis, Monographs on Applied and Computational Mathematics, vol. 2, University Press, Cambridge, 1998.

[1] W.-J. Beyn, On the numerical approximation of phase portraits near stationary points, SIAM J. Numer. Anal. 24 (1987), no. 5, 1095–1112.

[2] W.-J. Beyn and J. Lorenz, Center manifolds of dynamical systems under discretization, Numer. Funct. Anal. Optimization 9 (1987), 381–414.

[3] P.E. Kloeden and J. Lorenz, Stable attracting sets in dynamical systems and in their one-step discretizations, SIAM J. Numer. Anal. 23 (1986), no. 5, 986–995.

Prüfungsinformationen

Beurteilungsschema

Note/Grade Benotungsschema

Position 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)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Fach: Applied Analysis (Wahlfach)
      • 4.12 Seminar in Analysis ( 2.0h SE / 4.0 ECTS)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Fach: Applied Mathematics (Wahlfach)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
  • Masterstudium Technische Mathematik (SKZ: 401, Version: 13W.1)
    • Fach: Seminar und Praktikum (Pflichtfach)
      • Seminar ( 2.0h SE / 4.0 ECTS)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
  • 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)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)

Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung

Wintersemester 2017/18
  • 312.190 SE Seminar aus Analysis (2.0h / 4.0ECTS)
Wintersemester 2016/17
  • 312.190 SE Seminar aus Analysis (2.0h / 4.0ECTS)
Wintersemester 2014/15
  • 312.190 SE Seminar aus Analysis (2.0h / 4.0ECTS)