312.224 (16W) Selected Topics in Analysis

Wintersemester 2016/17

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First course session
04.10.2016 13:30 - 16:00 N.1.25 On Campus
... no further dates known

Overview

Lecturer
Course title german Ausgewählte Kapitel der Analysis (Nichtlineare Analysis)
Type Lecture - Practical class (continuous assessment course )
Hours per Week 3.0
ECTS credits 5.0
Registrations 4 (15 max.)
Organisational unit
Language of instruction Englisch
Course begins on 04.10.2016

Time and place

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Course Information

Course content

Description

We investigate various methods for the analysis of abstract nonlinear equations in Banach spaces. In concrete situations, these equations are ordinary or partial differential equations, as well as integral equations.

Contents

Topological methods: Brouwer and Leray-Schauder degree, Measures of Noncompactness

Calculus in Banach spaces: Analysis in normed spaces, Taylor’s theorem, implicit mapping theorem

Local bifurcation theory: Fredholm operators, Lyapunov-Schmidt method, Fold bifurcation, Bifurcation from simple eigenvalues

Monotone operators: Basics, Krein-Rutman theorem

Literature

tba

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)
        • 312.224 Selected Topics in Analysis (3.0h VU / 5.0 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 (3.0h VU / 5.0 ECTS)

Equivalent courses for counting the examination attempts

This course is not assigned to a sequence of equivalent courses