Infopaket

Mathematical analysis

ОК.11

Обов’язкова дисципліна для ОП

First

2022/2023

1 Semester

13

PLO 2 To use the modern mathematical apparatus of continuous and discrete analysis, linear algebra, analytical geometry, in professional activity to solve problems of a theoretical and applied nature in the process of designing and implementing informatization objects.

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 the beginnings of analysis, geometry.

Part 1. The limit of a numerical sequence Problems of mathematical analysis The set of real numbers The limit of a numerical sequence Ordinal and arithmetic properties of the limit of a numerical sequence The limit of a monotonic sequence Cauchy's criterion and Stolz's theorem Part 2. Limit and continuity of a function Continuity of function Properties of continuous functions The limit of a function at a point Properties of the boundary of a function at a point Uniformly continuous functions Part 3. Differential calculus The derivative of a function and its properties Basic theorems of differential calculus Derivatives and differentials of higher orders Convex functions The application of the derivative to the study of the properties of the function and the construction of its graph Part 4. The Newton-Leibnitz primordial and integral The original Elementary methods of integration Integration of rational functions Integration of irrational functions by the method of rationalization Integration of trigonometric functions and their rational combinations Part 5. The Riemann integral Riemann and Darboux integrals The Riemann integrability criterion and the simplest properties of the Riemann integral Properties of the Riemann integral Application of the Riemann integral Part 6. Functions of many variables Functions of many variables Limit and continuity of a function of many variables Derivative and differential of functions of many variables Derivatives and differentials of higher orders Extrema of functions of many variables Implicit mappings Conditional extrema of functions of many variables Part 7. Rows Series with integral members Series with terms of arbitrary sign Functional sequences and series Properties of uniformly convergent functional sequences and series. Power series

1. Rubl-ov B.V. Matematichnii analіz. Teorіia poslіdovnostei. – Kiїv, KNU, 2010 – 95 s. 2. Pіdkuiko S.І. Matematichnii analіz. – L-vіv, Galits-ka Vidavnicha Spіlka, 2004 – 530 s. 3. Aleksandrovich І.M. ta іn. Vstup do matematichnogo analіzu. Zbіrnik zadach. - Kiїv "Kiїvs-kii unіversitet". – 2018. – 239 s. 4. Dorogovtsev A.Ia. Matematicheskii analiz. Kratkii kurs v sovremennom izlozhenii. – Kiev, Fakt, 2004 – 560 s. 5. Fikhtengol-ts G.M. Osnovy matematicheskogo analiza. 2 toma – Moskva, Nauka, 1 tom 1968 – 440 s, 2 tom 1968 – 464 s. 6. Liashko S.I., Boiarchuk A.K. i dr. Sbornik zadach i uprazhnenii po matematicheskomu analizu – Moskva-Sankt-Peterburg-Kiev, Dialektika, 2001 – 432 s. 7. Demidovich B.P. Sbornik zadach i uprazhnenii po matematicheskomu analizu – Moskva, Nauka, 1977 – 528 s.

Lectures, practical, consultations, independent work

Semester assessment: First semester: 1) Control work I: РН1.1, РН1.2, РН2.1, РН3.1 – 10 points / 6 points; 2) Control work II: РН1.1, РН1.2, РН2.1, РН3.1 – 10 points / 6 points; 3) Control work III: РН1.1, РН1.2, РН2.1, РН3.1 – 10 points / 6 points; 4) Assessment for practical classes: РН2.1, РН3.1, РН4.1 – 30 points / 18 points. Second semester: 1) Control paper IV: РН1.1, РН1.2, РН2.1, РН3.1 – 10 points / 6 points; 2) Control paper V: РН1.1, РН1.2, РН2.1, РН3.1 – 10 points / 6 points; 3) Control work VI: РН1.1, РН1.2, РН2.1, РН3.1 – 10 points / 6 points; 4) Assessment for practical classes: РН2.1, РН3.1, РН4.1 – 30 points / 18 points. - final evaluation (in the form of an exam in each semester): - the maximum number of points that can be obtained by a student: 40; - learning outcomes that are evaluated: PH1.1, PH1.2, PH2.1, PH3.1; PH4.1; - form of conduct: written work; - types of tasks: theoretical questions (5 to 8%, together 40%), tasks (20% and 40%, together 60%).

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