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This entry is from Winter semester 2018/19 and might be obsolete. No current equivalent could be found.

Applied Functional Analysis
(dt. Angewandte Funktionalanalysis)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Written or oral examination
Examination type: Successful completion of at least 50 percent of the points from the weekly exercises.
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with Functional Analysis
Person in charge of the module's outline Prof. Dr. Ilka Agricola, Prof. Dr. Stephan Dahlke

Contents

Banach and Hilbert spaces, theorems of Hahn and Banach, function spaces, continuation and embedding theorems, elliptic partial differential equations


Qualification Goals

The students shall

  • learn to recognize and assess the relevance of functional analytical methods for practical problems, e.g. from numerical analysis, , and to acquire the functional analytical tools to solve these problems,
  • learn how methods of linear algebra, analysis and topology interact,
  • Re-evaluate knowledge from the basic modules and some advanced modules (e.g. ''complex analysis and vector analysis''),
  • recognize the relationships of functional analysis to other areas of mathematics and other sciences,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden und Kenntnisse der allgemeinen Integrationstheorie aus Maß- und Integrationstheorie oder Funktionentheorie und Vektoranalysis.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics
  • LAaG Mathematics

When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.

The module can also be used in other study programs (export module).

Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Angewandten Mathematics zugeordnet ist.


Recommended Reading

  • Dobrowolski, M., Angewandte Funktionalanalysis, Springer 2006
  • Alt, H.W. , Lineare Funktionalanalysis, Springer 1999



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2018/19. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.