Infopaket

Integral theory

ВК.1.01

Вибіркова дисципліна для ОП

First

2024/2025

5 Semester

5

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", "Mathematical Analysis 2" and "Topology of the Real Line and Measure Theory", in particular, the geometric properties of the number line, the theory of the Riemann integral on the line, the theory of the Riemann multiple integral, the abstract theory of measure, the theory of Lebesgue measure on the real line and the plane. 2) Be able to solve problems within the framework of the school mathematics course, the university courses "Mathematical Analysis 1", "Mathematical Analysis 2" and "Topology of the Real Line and Measure Theory".

1 Definition of a measurable function. Examples 2 Borel functions. Functions measurable by Lebesgue 3 Properties of measurable functions. 4 Convergence almost everywhere 5 Convergence in measure 6 Systematization and repetition Lebesgue integral 1 Definition of a Lebesgue integral. Examples 2 Properties of a Lebesgue integral 3 Basic limit theorems8 4 Comparison of the Riemann integral and the Lebesgue integral 5 Lebesgue-Stieltjes integral 7 Systematization and repetition

Main 2. Radchenko V.M. Teoriya miry ta intehrala. — K.: Kyyivskyy universytet, 2012. – 144 s. Additional 7. Zavdannya do praktychnykh zanyat z teoriyi miry ta intehrala dlya studentiv spetsialnostey „matematyka i „statystyka” mekhaniko-matematychnoho fakultetu / Ukladachi O.Yu.Konstantinov, O.H.Kukush, O.O.Kurchenko, O.N.Nesterenko, V.M.Radchenko, T.O.Petrova, A.V.Chaykovskyy. — K.: VPTs „Kyyivskyy universytet”, 2019. — 80 c. 10. Lyashko I.I., Yemelyanov V.F., Boyarchuk O.K Matematychnyy analiz. 2 chastyny – Kyyiv, Vyshcha shkola, 1 chastyna 1992. – 495 s, 2 chastyna 1993. – 375 s.

Lectures. Seminars. Consultations. Independent work

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