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Functional and Numerical Analysis (FOMICS block course)

Description

COURSE OBJECTIVES

Understanding the basic elements of Functional Analysis.

 

COURSE DESCRIPTION

This course provides a concise introduction to some prominent subjects in functional analysis theory and some applications to the analysis and numerical solution of partial differential equations (PDEs). Starting from Banach spaces and basic topological considerations, we will consider linear and bounded 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. On the PDE side, we will introduce the Lebesgue integral, Sobolev-spaces, and Galerkin discretization for linear elliptic PDEs.

 

LEARNING METHODS

Following the lecture. Reading text books. Exercising by doing independent work and following exercises. Attending tutorials.

 

EXAMINATION INFORMATION
Graded assignments and final written exam (closed book)

 

REFERENCES

  • Rudin, Walter. Functional Analysis. McGraw-Hill, 1991
  • Script provided in the lecture
  • Markus Haase, Functional Analysis: An Elementary Introduction, AMS

People

 

Krause R.

Course director

Additional information

Semester
Spring
Academic year
2021-2022
ECTS
3
Language
English
Education
Master of Science in Computational Science, Elective course, 1st year
Master of Science in Computational Science, Elective course, 2nd year
PhD programme of the Faculty of Informatics, PhD course, Lecture, 1st year
PhD programme of the Faculty of Informatics, PhD course, Lecture, 2nd year