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Theory of functions of a complex variable

ННД.17

Обов’язкова дисципліна для ОП

First

2023/2024

5 Semester

5

LO 2. To have basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, theory of differential equations, in particular partial differential equations, probability theory, mathematical statistics and random processes, numerical methods. LO 13. To use specialized software products and software systems of computer mathematics in practical work.

Full-time form

Successful completion of courses: 1. Mathematical analysis. 2. Algebra and geometry. Knowledge: 3. Elementary school mathematics. 4. Basic definitions and theorems of mathematical analysis, algebra and geometry. Skill: 5. Solve problems of mathematical analysis, algebra and geometry. 6. Investigate functions for continuity and differentiability. 7. Expand the functions of a real variable into a Taylor series.

Topic 1. Complex numbers. Repetition. Topic 2. Functions of a complex variable. Continuity. Topic 3. Cauchy-Riemann conditions. Harmonic functions Topic 4. Conformal mappings. An entire linear function. Fractional linear function Topic 5. Fractional-linear function Topic 6. Power and fractional-linear functions. The simplest areas with cuts. Zhukovsky's function. Topic 7. Transcendent functions Topic 8. Integral along a curve, Cauchy's integral theorem, Cauchy's integral formula. Topic 9. Power series. Development of analytical functions in the Taylor series. The unity theorem. Zeros of analytical functions Topic 10. Development of analytic functions in the Laurent series Topic 11. Special points of an unambiguous nature Topic 12. Remainders of analytical functions Topic 13. The main theorem on remainders Topic 14. Calculation of integrals

1. Volkovyskii L.I., Lunts G.L., Aramovich I.G. Sbornik zadach po teorii funktsii kompleksnogo peremennogo, 2004. 2. Grishchenko O.Iu., Onots-kii V.V. Kurs lektsіi z kompleksnogo analіzu. Kiїv, 2015. 3. Samoilenko V.G. ta іn. Diferentsіiuvannia funktsіi kompleksnoї zmіnnoї. Konformnі vіdobrazhennia: Metodichnі vkazіvki do praktichnikh zaniat- z kursu "Kompleksnii analіz" dlia studentіv mekhanіko-matematichnogo fakul-tetu, VPТs "Kiїvs-kii unіversitet", 2002. 4. Samoilenko V.G. ta іn. Riadi ta іntegrali v kompleksnіi ploshchinі : Metodichnі vkazіvki do praktichnikh zaniat- z distsiplіni "Kompleksnii analіz" dlia studentіv mekhanіko-matematichnogo fakul-tetu, VPТs "Kiїvs-kii unіversitet", 2002.

Lectures, practical classes, independent work

Semester assessment: The maximum number of points that can be obtained by a student: 60 points: 1. Control work 1: PH 1.1, PH 1.2, PH2.1 – 15 points. 2. Control work 2: PH 1.3, PH 1.4, PH 1.5, PH 2.2, PH 2.3, PH 2.4 – 15 points. 3. Assessment in practical classes: PH 1.1, PH 1.2, PH 1.3, PH 1.4, PH 1.5, PH2.1, РН 2.2, РН 2.3, РН 2.4, PH3.1, РН 3.2, РН 3.3 – 15 points. 4. Assessment of independent work: PH 1.1, PH 1.2, PH 1.3, PH 1.4, PH 1.5, PH2.1, PH 2.2, PH 2.3, PH 2.4, PH 4.1, PH 4.2, PH 4.3 - 15 points. Final assessment (in the form of an exam) 1. The maximum number of points that can be obtained by a student: 40 points. 2. Learning outcomes to be evaluated: PH1.1, PH1.2, PH1.3, PH1.4, PH1.5, PH2.1, PH2.2, PH2.3, PH2.4. 3. Form of conduct and types of tasks: written, 4 practical tasks (10 points each).

Ukrainian