Infopaket

Harmonic analysis

ВК.1.02

Вибіркова дисципліна для ОП

First

2024/2025

6 Semester

4

RN1. Demonstrate knowledge and understanding of the basic concepts, principles, theories of fundamental and applied mathematics and use them in practice. RN2. Possess the basic principles and methods of mathematical, complex and functional analysis ... RN14. Demonstrate the ability for self-study and continued professional development. RN15. Be able to organize one's own activities and obtain results within a limited time. RN16. Demonstrate skills in interacting with other people, the ability to work in teams. RN18. Effectively communicate information, ideas, problems and solutions with specialists and society in general. RN20. Demonstrate professional communication skills, including oral and written communication in Ukrainian and at least one other common European language.

1) Know the material of the courses "Mathematical Analysis 1" and "Mathematical Analysis 2", in particular, series theory, Riemann integral theory on a straight line, Riemann improper integral theory, basic concepts of functional analysis. 2) Be able to solve problems of the university courses "Mathematical Analysis 1" and "Mathematical Analysis 2".

Trigonometric Fourier series 1 Trigonometric polynomial, Fourier series 2 Convergence of Fourier series, Fourier integral, Fourier transform 3 Feuer and Weierstrass theorems, Vallée-Poussin averages 4 Fourier series for functions with bounded variation, differentiation and integration of Fourier series Fourier series in Hilbert spaces 1 Hilbert space 2 Fourier series in Hilbert space 3 Bessel inequality, best approximation in Hilbert space 4 Systematization, generalization and repetition

Main 1. Lyashko I.I., Yemelyanov V.F., Boyarchuk O.K Matematychnyy analiz. 2 chastyny – K.: Vyshcha shkola, 1 chastyna 1992. – 495 s, 2 chastyna 1993. – 375 s. ..

Lectures. Seminars. Consultations. Independent work.

Forms of student assessment: Semester assessment: 1) modular test paper I – 25 points 2) modular test paper II – 25 points 3) summary score for practical classes – 10 points 4) additional points – up to 15 points Summary assessment in the form of an exam: – 40 points Conditions for admitting students to the final exam: at least 36 points for the semester assessment. Conditions for obtaining an overall positive grade in the discipline: at least 24 points on the final exam.

Ukrainian