Jul 18, 2019   3:56 p.m. Kamila
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Course syllabus D1-FA - Functional analysis (FCE - 2019/2020 - post-graduate studies)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit title: Functional analysis
Course unit code: D1-FA
Mode of completion and Number of ECTS credits: Exam-PhD (5 credits)
 
Name of lecturer: doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer, tutor) - slovak, english
prof. RNDr. Karol Mikula, DrSc. (person responsible for course)
 
Learning outcomes of the course unit:
The student gains knowledge of Hilbert space theory, theory of linear and metric spaces, theory of linear operators and functionals, Sobolev functional spaces. He will be familiar with variational formulation of elliptic boundary value problems, existence theory of variational solutios and convergence of numerical solutions.
 
Prerequisites and co-requisites: none
 
Course contents:
- Hilbert, linear, norm and metric spaces.
- Linear operators and functionals, their properties.
- Riesz theorem, Minima quadratic functional theorem.
- Sobolev spaces, traces.
- Variational formulation of elliptic boundary value problems.
- Existence of variational solutions for elliptic problems, Lax-Milgram theorem.
- Ritz and Galerkin method.
 
Recommended or required reading:
Basic:
REKTORYS, K. Variační metody v inženýrských problémech a v problémech matematické fyziky. Praha : SNTL, 1974. 600 p.
KUFNER, A. -- JOHN, O. -- FUČÍK, S. Function Spaces. Praha : ČSAV, 1977. 454 p.

 
Planned learning activities and teaching methods: Seminar: 26 hours per semester (on-site method).
 
Assesment methods and criteria: exam
 
Language of instruction: Slovak, English
 
Work placement(s): There is no compulsory work placement in the course unit.


Last modification made by Ing. Peter Korčák on 10/31/2017.

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