Course detail
Fourier Analysis
FSI-SFA-AAcad. year: 2021/2022
The course is devoted to basic properties of Fourier Analysis and illustrations of its techniques on examples. In particular, problems on reprezentations of functions, Fourier and Laplace transformations, their properties and applications are studied.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course-unit credit is awarded on condition of having attended the seminars actively and passed the control test.
Examination has a practical and a theoretical part. In the practical part student has to illustrate the given tasks on particular examples.
Theoretical part includes questions related to the subject-matter presented at the lectures.
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
A. N. Kolmogorov, S. V. Fomin: Základy teorie funkcí a funkcionální analýzy, SNTL, Praha 1975. (CS)
E. W. Howel, B. Keneth: Principles of Fourier Analysis, CRC Press, 2001. (EN)
I. P. Natanson: Teorija funkcij veščestvennoj peremennoj, [Theory of functions of a real variable] ,Third edition, "Nauka'', Moscow, 1974. (RU)
Recommended reading
Elearning
Classification of course in study plans
- Programme N-MAI-P Master's 1 year of study, summer semester, compulsory
- Programme M2A-A Master's
branch M-MAI , 2 year of study, summer semester, compulsory
- Programme N-MAI-A Master's 1 year of study, summer semester, compulsory
2 year of study, summer semester, compulsory - Programme N-AIM-A Master's 2 year of study, summer semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
convergence theorems.
2. Space of quadratically integrable functions - different kinds of convergence, Fourier series.
3. Singular integral - definition, representation, application to Fourier series.
4. Trigonometric series.
5. Fourier integral.
6. Fourier transformation - Fourier transformation (FT), inverse formula, basic properties of FT, Hermit and Laguer functions, FT and convolution, applications.
7. Plancherel theorem, Hermit functions.
8. Laplace transformation.
Exercise
Teacher / Lecturer
Syllabus
2. Space of quadratically integrable functions - different kinds of convergence, Fourier series.
3. Singular integral - definition, representation, application to Fourier series.
4. Trigonometric series.
5. Fourier integral.
6. Fourier transformation - Fourier transformation (FT), inverse formula, basic properties of FT, Hermit and Laguer functions, FT and convolution, applications.
7. Plancherel theorem, Hermit functions.
8. Laplace transformation
Elearning