Infopaket

Mathematical analysis

ННД.10

Обов’язкова дисципліна для ОП

First

2021/2022

3 Semester

10

LO 1. Demonstrate knowledge and understanding of basic concepts, principles, and theories of fundamental and applied mathematics and use them in practice. LO 9. Build efficient algorithms regarding the accuracy of calculations, stability, speed and cost of system resources for numerical study of mathematical models and solution of practical problems.

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. 3) Master the material of the "Mathematical Analysis 1" course.

Topic 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 Topic Improper integrals and integrals dependent on a parameter Improper integrals Transformation and calculation of improper integrals Eigenintegrals dependent on the parameter Improper integrals dependent on the parameter Properties of functions defined by nonproprietary integrals dependent on a parameter Improper integrals depending on the parameter are important Topic Multiple, curvilinear and surface integrals Curvilinear integrals Double (multiple) integral Changing the variable in the double (multiple) integral Surface integrals Elements of Stokes theory Mir Lebesgue's theme Elements of the topology of a real line Basic classes of sets Generated classes of sets Measure Continuation of measure Lebesgue's measure Topic Dimensional functions and the Lebesgue integral Dimensional functions Sequences of measurable functions Convergence by measure The Lebesgue integral

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. Natanson I.P. Teoriia funktsii veshchenstvennoi peremennoi. – Moskva, Nauka, 1974 – 480 s. 6. Dorogovtsev A.Ia. Elementy obshchei teorii mery i integrala. – Kiev, Fakt, 2007 – 156 s. 7. Liashko I.I., Boiarchuk A.K., Gai Ia.G. i dr. Spravochnoe posobie po matematicheskomu analіzu. Chast- 1. Vvedenie v analіz, proizvodnaia, integral. – Kiev, Vishcha shkola, 1978 – 696 s. ..

Lectures, practical classes, consultations, independent work of students

Semester assessment: 1) modular control work I - 25 points 2) modular 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 obtaining an overall positive grade in the discipline: at least 24 points per final exam.

Ukrainian