312.190 (19W) Seminar in Analysis
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
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
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)
- 312.190 Seminar in Analysis (2.0h SE / 4.0 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: 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)
-
4.12 Seminar in Analysis (
2.0h SE / 4.0 ECTS)
-
Subject: Applied Analysis
(Compulsory elective)
- 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)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
-
Subject: Applied Mathematics
(Compulsory elective)
- 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)
-
Seminar (
2.0h SE / 4.0 ECTS)
-
Subject: Seminar und Praktikum
(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)
- 312.190 Seminar in Analysis (2.0h SE / 4.0 ECTS)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
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)