312.224 (20S) Selected Topics in Analysis (Chaos and Order)

Sommersemester 2020

Registration deadline has expired.

First course session
03.03.2020 13:00 - 15:00 N.2.01 On Campus
... no further dates known

Overview

Lecturer
Course title german Ausgewählte Kapitel der Analysis (Chaos und Ordnung)
Type Lecture
Hours per Week 2.0
ECTS credits 3.0
Registrations 7
Organisational unit
Language of instruction English
possible language(s) of the assessment English
Course begins on 03.03.2020
eLearning Go to Moodle course

Time and place

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Course Information

Intended learning outcomes

The course provides an introduction into the mathematical stability and chaos theory. Attendees obtain a rigorous understanding of notions like the "butterfly effect" from popular sciences and learn how and when not to trust numerical simulations. 

Teaching methodology including the use of eLearning tools

Chalk and Blackboard,  a computer simulation when appropriate

Course content

1 Difference equations (difference equations and solutions, autonomous difference equations and mappings, linear difference equations)

2 Stability (stability notions, stability of linear equations, linearized stability, global stability)

3 Autonomous dynamics (periodic points, invariant and limit sets, topological conjugation, symbolic dynamics, chaotic dynamics)

4 Scalar autonomous difference equations (differentiable dynamics on the real line, bifurcation of fixed points, the logistic family)

Prior knowledge expected

Analysis (topology in metric spaces), Linear Algebra

Curricular registration requirements

Interest in mathematics

Literature

R.L. Devaney: An Introduction to Chaotic Dynamical Systems, Benjamin/Cummings Publishing Company, Menlo Park, 1986

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.

Modified examination information (exceptional COVID-19 provisions)

For the period in which face-to-face exams are not possible, exams for this course are held online via BigBlueButton in accordance with the guidelines at https://www.aau.at/corona/pruefungen. The examination will consist entirely of an oral part. 

Examination methodology

Oral exam

Examination topic(s)

Contents of the lecture notes, theorems, proofs and examples

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)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 ECTS)
  • Bachelorstudium Technische Mathematik (SKZ: 201, Version: 17W.1)
    • Subject: Angewandte Analysis (Compulsory elective)
      • 8.5 Ausgewählte Kapitel der Analysis ( 2.0h VO / 3.0 ECTS)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 ECTS)
          Absolvierung im 5., 6. Semester empfohlen
  • Bachelor's degree programme Technical Mathematics (SKZ: 201, Version: 12W.2)
    • Subject: Angewandte Analysis (Compulsory elective)
      • Ausgewählte Kapitel der Analysis ( 3.0h VU / 5.0 ECTS)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 4.9 Selected Topics in Analysis ( 2.0h VO / 3.0 ECTS)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Mathematics (Compulsory elective)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 ECTS)
  • Master's degree programme Technical Mathematics (SKZ: 401, Version: 13W.1)
    • Subject: Angewandte Analysis (Compulsory elective)
      • Ausgewählte Kapitel der Analysis ( 3.0h VU / 5.0 ECTS)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 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)
        • 312.224 Selected Topics in Analysis (Chaos and Order) (2.0h VO / 3.0 ECTS)

Equivalent courses for counting the examination attempts

This course is not assigned to a sequence of equivalent courses