Feb 17, 2020   8:00 a.m. Miloslava
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Course syllabus B1-FUA - Functional analysis (FCE - WS 2019/2020)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit title: Functional analysis
Course unit code: B1-FUA
Mode of completion and Number of ECTS credits: Exam (5 credits)
 
Name of lecturer: doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer, person responsible for course, tutor) - slovak, english
Ing. Matej Medľa, PhD. (examiner, instructor)
Ing. Mgr. Lukáš Tomek, PhD. (examiner, instructor)
 
Learning outcomes of the course unit:
The lectures consist of explaining the main results of Hilbert space theory, theory of linear and metric spaces, then theory of linear operators and functionals following by Sobolev functional spaces. Second part is devoted to the theory of variational formulation of elliptic boundary value problems, existence theory of variational solutios and convergence of numerical solutions.
 
Prerequisites and co-requisites: passed Ordinary differential equations and passed Partial differential equations
 
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.
 
Recommended or required reading:
Basic:
REKTORYS, K. Variační metody v inženýrských problémech a v problémech matematické fyziky. Praha : Academia, 1974. 600 p.
KUFNER, A. -- JOHN, O. -- FUČÍK, S. Function Spaces. Praha : ČSAV, 1977. 454 p.

 
Planned learning activities and teaching methods: lectures, lessons
3/2 - 65 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 02/28/2019.

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