Oct 22, 2020   12:07 p.m. Sergej

# Course syllabus D1-FA - Functional analysis (FCE - 2020/2021 - post-graduate studies)

Information sheet          ECTS          Syllabus

Slovak          English

University:
Slovak University of Technology in Bratislava
Faculty:
Course unit code:
D1-FA
Course unit title:
Functional analysis
Mode of delivery, planned learning activities and teaching methods:
 workshop 2 hours weekly / 26 hours per semester of study (on-site method)

Credits allocated: 5

Recommended semester/trimester: Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics - doctoral (semi-compulsory), 1. year
Level of study:
3.
Prerequisites for registration:
none

Assesment methods:
Correct elaboration of all given tasks, exam.

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.

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.

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.

Language of instruction: slovak and english or english

Notes:

Courses evaluation:
Assessed students in total: 6

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Name of lecturer(s):
doc. RNDr. Angela Handlovičová, PhD. (examiner, instructor, lecturer, tutor) - slovak, english
prof. RNDr. Karol Mikula, DrSc. (person responsible for course)

Last modification: 31. 3. 2020
Supervisor:
prof. RNDr. Karol Mikula, DrSc. and programme supervisor

Last modification made by Ing. Marián Dubík on 03/31/2020.

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