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[Nonlinear Functional Analysis] - [2015 Sommer]

Module Code
MH01
Name
Nonlinear Functional Analysis
Credit Points
8 CP
Workload
240
Duration
1 semester
Cycle
0
Methods Lecture 4 h + Exercise course 2 h
Objectives To have a firm command of the main topics in Nonlinear Functional Analysis.
Content • Existence theorems: inverse function theorem, implicit function theorem, Sard’s theorem • Fredholm operators: Fredholm operators, Smale’s version of Sard’s theorem and applications. • Topological degree theory: Brouwer’s degree theory, Leray–Schauder’s degree theory, applications.
Learning outcomes The capability of solving problems in the underlying field. The capability to present the solutions in the exercise courses.
Prerequisites
Suggested previous knowledge Partial Differential Equations, Functional Analysis (MC3)
Assessments Homework consisting of solving exercises and a written or oral examination at the end of the term.
Literature Louis Nirenberg: Topics in Nonlinear Functional Analysis
Melvyn S. Berger: Nonlinearity and Functional Analysis
Claus Gerhardt: Analysis II
Claus Gerhardt: Curvature Problems
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