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Functional and Numerical Analysis (FOMICS block course)

Description

COURSE OBJECTIVES
Obtain knowledge on: central concepts and ideas of linear functional analysis; Banach spaces, bounded operators; compact operators; duality and representation; spectral theory

 

COURSE DESCRIPTION
This course provides a concise introduction to some prominent subjects in functional analysis. Starting from Banach spaces and basic topological considerations, we will consider linear and bounded operators, compact operators, and dual spaces, as well as some classical fixed-point results. We then will introduce Hilbert spaces, scalar products, and the Lax-Milgram theorem. Eventually, we will present some results from spectral theory.

LEARNING METHODS
Lecture, reading, self study, discussion, tutorial, written assignments

 

EXAMINATION INFORMATION
Graded assignments

 

REFERENCES

  • Lang: Real and Functional Analysis, Springer 1993
  • Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer 2010
  • Bogachev, Smolyanov: Real and Functional Analysis, Springer 2020

 

People

 

Krause R.

Course director

Additional information

Semester
Spring
Academic year
2020-2021
ECTS
3
Language
English
Education
Master of Science in Computational Science, Elective course, Lecture, 1st year
Master of Science in Computational Science, Elective course, Lecture, 2nd year
PhD programme of the Faculty of Informatics, Elective course, Lecture, 1st year
PhD programme of the Faculty of Informatics, Elective course, Lecture, 2nd year