Complex analysis

Course: Applied Mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Complex analysis
Code
Module type
Обов’язкова дисципліна для ОП
Educational cycle
First
Year of study when the component is delivered
2023/2024
Semester/trimester when the component is delivered
5 Semester
Number of ECTS credits allocated
5
Learning outcomes
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.
Form of study
Prerequisites and co-requisites
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.
Course content
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.
Recommended or required reading and other learning resources/tools
1. Volkovыskyi L.Y., Lunts H.L., Aramovych Y.H. Sbornyk zadach po teoryy funktsyi kompleksnoho peremennoho, 2004. 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.
Planned learning activities and teaching methods
Lectures, independent work, literature processing, homework.
Assessment methods and criteria
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).
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Departments

The following departments are involved in teaching the above discipline