Jan 24, 2020   6:42 a.m. Timotej

# Course syllabus B1-FUA - Functional analysis (FCE - WS 2019/2020)

Information sheet          ECTS          Syllabus

Slovak          English

University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit code: B1-FUA
Course unit title: Functional analysis
Mode of delivery, planned learning activities and teaching methods:
 lecture 3 hours weekly (on-site method) seminar 2 hours weekly (on-site method)

Credits allocated: 5

Recommended semester/trimester: Mathematical and Computational Modeling - bachelor (compulsory), 5. semester
Level of study: 1.
Prerequisites for registration: passed Ordinary differential equations (B1-ODR) and passed Partial differential equations (B1-PDR)

Assesment methods:
Correct elaboration of two given tests.
Minimum of 56 points obtained at the exam.

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.

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.

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.

Language of instruction: slovak or english

Notes:

Courses evaluation:
Assessed students in total: 30

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16,7 %10,0 %26,7 %30,0 %16,6 %0 %
Name of lecturer(s): 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)

Last modification: 28. 2. 2019
Supervisor: doc. RNDr. Angela Handlovičová, PhD. and programme supervisor

Last modification made by Ing. Peter Korčák on 02/28/2019.

 Type of output: PDF output (PDF)Document RTF (RTF)XML format for IS (XML IL)