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Complex analysis

Обов’язкова дисципліна для ОП

First

2021/2022

5 Semester

5

LO 2. Be able to use basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, and differential equations, including partial differential equations, probability theory, mathematical statistics and random processes, numerical methods. LO 13. Use specialized software products and software systems of computer mathematics in research.

Distance form

To successfully learn the discipline “Complex Analysis” a student should satisfy the following requirements. He/She have successfully passed the courses “Mathematical Analysis”, “Algebra and Geometry”. He/She knows the elementary school mathematics and the essential theorems and definitions of Mathematical Analysis, Algebra and Geometry. He/She is able to solve basic exercises in Mathematical Analysis, Algebra and Geometry, to examine continuity and differentiability of a function, to find a Taylor series of a function.

Mapping of the regions of a complex plane, in particular using conformal functions, application of Cauchy-Riemann condition, investigation of continuity and analyticity, constructing Taylor and Laurent series for an analytical functions, determination of zeros and singular points of analytic functions, residuals computation, application of residuals theory to calculation of integrals.

2. Hryshchenko O.Iu., Onotskyi V.V. Kurs lektsii z kompleksnoho analizu. Kyiv, 2015. 3. Samoilenko V.H. ta in. Dyferentsiiuvannia funktsii kompleksnoi zminnoi. Konformni vidobrazhennia: Metodychni vkazivky do praktychnykh zaniat z kursu "Kompleksnyi analiz" dlia studentiv mekhaniko-matematychnoho fakultetu, VPTs «Kyivskyi universytet», 2002. 4. Samoilenko V.H. ta in. Riady ta intehraly v kompleksnii ploshchyni : Metodychni vkazivky do praktychnykh zaniat z dystsypliny "Kompleksnyi analiz" dlia studentiv mekhaniko-matematychnoho fakultetu, VPTs «Kyivskyi universytet», 2002.

Lectures, independent work, literature processing, homework.

Intermediate assessment: The maximal number of available points is 60. Test work no. 1: RN 1.1, RN 1.2, RN 2.1 – 15 points. Test work no. 2: RN 1.3, RN 1.4, RN 1.5, RN2.2, RN2.3, RN 2.4 – 15 points. Assessment during practical lessons: RN 1.1, RN 1.2, RN 1.3, RN 1.4, RN 1.5, RN 2.1, RN 2.2, RN 2.3, RN 2.4, RN 3.1, RN 3.2, RN 3.3 – 15 points Assessment of student’s independent work: RN 1.1, P RN H 1.2, RN 1.3, RN 1.4, RN 1.5, RN 2.1, RN 2.2, RN 2.3, RN 2.4, RN 4.1, RN 4.2, RN 4.3 – 15 points. Final assessment (in the form of exam): The maximal number of available points is 40. The results of study to be assessed are RN 1.1, RN 1.2, RN 1.3, RN 1.4, RN 1.5, RN 2.1, RN 2.2, RN 2.3, RN 2.4. The form of exam: writing. The types of assignments are 4 writing assignments (all practical, 10 points each).

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