Infopaket

Mathematical analysis 1

ОК.09

Обов’язкова дисципліна для ОП

First

2022/2023

1 Semester

17

LO 2 To have the basic provisions and methods of mathematical, complex and functional analysis. LO 10 To master the methods of choosing rational methods and algorithms for solving mathematical problems of optimization, operations research, optimal management and decision-making, data analysis.

Full-time form

1) Know the content of the school course in mathematics, algebra and the beginnings of analysis, geometry. 2) To be able to solve problems within the school course of mathematics, algebra and beginnings analysis, geometry.

Introduction to mathematical analysis 1 Method of mathematical induction 2 Binary relations 3 Function and its graph, polar coordinate system 4 Ordered space 5 The real axis as an ordered space 6 The first concepts of topology on the real axis 7 Limit of a numerical sequence, different methods of finding the limit of a sequence 8 Monotonic, bounded sequences, Weierstrass theorem 9 Cauchy's criterion, Stolz's theorem 10 Subsequences, upper and lower bounds of a sequence, Bolzano-Wenierstrass theorem 11 Limit of a function at a point, definition of Cauchy and Heine 12 Landau symbols, different methods of finding the limit of a function at a point 13 Continuity of a function at a point and on an interval 14 Properties of continuous functions on the interval, Cauchy and Weierstrass theorems 15 Uniformly continuous functions Derivative function 1 Derivative of a function and its properties 2 Basic theorems of differential calculus, differential 3 Derivatives and differentials of higher orders 4 Theorems about the average 5 Convex functions, different methods of proving inequalities 6 Application of the derivative to the study of the properties of the function and construction of its graph The Newton-Leibnitz primitive and integral 1 Original. Elementary methods of integration 2 Integration of rational functions 3 Integration of irrational functions by the method of rationalization 4 Integration of trigonometric functions and their rational combinations 5 Primary in a broad sense The Riemann integral 1 Riemann and Darbou integrals, integral sums 2 Criterion of Riemann integrability and properties of the Riemann integral 3 Finding the Riemann integral 4 Theorems about the mean for the Riemann integral 5 Application of the Riemann integral Functions of many variables Rows

1. Dorogovtsev A.Ia. Matematicheskii analiz. Kratkii kurs v sovremennom izlozhenii. – Kiev, Fakt, 2004 – 560 s. 2. Fikhtengol-ts G.M. Osnovy matematicheskogo analiza. 2 toma – Moskva, Nauka, 1 tom 1968 – 440 s, 2 tom 1968 – 464 s. 3. Liashko S.I., Boiarchuk A.K. i dr. Sbornik zadach i uprazhnenii po matematicheskomu analizu – Moskva-Sankt-Peterburg-Kiev, Dialektika, 2001 – 432 s. 4. Demidovich B.P. Sbornik zadach i uprazhnenii po matematicheskomu analizu – Moskva, Nauka, 1977 – 528 s. 5. Liashko I.I., Boiarchuk A.K., Gai Ia.G. i dr. Spravochnoe posobie po matematicheskomu analizu. Chast- 1. Vvedenie v analiz, proizvodnaia, integral. – Kiev, Vishcha shkola, 1978 – 696 s. 6. Liashko I.I., Boiarchuk A.K., Gai Ia.G. i dr. Spravochnoe posobie po matematicheskomu analizu. Chast- 2. Riady, funktsii neskol-kikh peremennykh, kratnye i krivolineinye integraly. – Kiev, Vishcha shkola, 1979 – 736 s.

Lectures, practical and independent work

Student evaluation forms: Semester assessment: 1) control paper I – 25 points 2) control work II – 25 points 3) combined assessment for practical classes – 10 points 4) additional points - up to 15 points Final assessment in the form of an exam: – 40 points Conditions for admitting students to the final exam: at least 36 points per semester assessment Conditions for receiving an overall positive grade in the discipline: at least 24 points per final exam.

Ukrainian