312.190 (19W) Seminar in Analysis

Wintersemester 2019/20

Registration deadline has expired.

First course session
28.02.2020 12:00 - 18:00 N.2.01 On Campus
... no further dates known

Overview

Lecturer
Course title german Seminar in Analysis
Type Seminar (continuous assessment course )
Hours per Week 2.0
ECTS credits 4.0
Registrations 3 (15 max.)
Organisational unit
Language of instruction English
possible language(s) of the assessment English
Course begins on 28.02.2020

Time and place

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Course Information

Intended learning outcomes

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

Teaching methodology including the use of eLearning tools

Talks based on the references below

Course content

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

Prior knowledge expected

Dynamical Systems, Numerical Analysis of ODEs

Literature

[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.

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.

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)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 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)
    • Subject: Applied Mathematics (Compulsory elective)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
  • Master's degree programme Technical Mathematics (SKZ: 401, Version: 13W.1)
    • Subject: Seminar und Praktikum (Compulsory subject)
      • Seminar ( 2.0h SE / 4.0 ECTS)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 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)
        • 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)

Equivalent courses for counting the examination attempts

Sommersemester 2022
  • 312.190 SE Seminar in Analysis (2.0h / 4.0ECTS)
Sommersemester 2021
  • 312.190 SE Seminar in Analysis (2.0h / 4.0ECTS)
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)