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Special topics of higher mathematics

ОК 09

Обов’язкова дисципліна для ОП

First

2023/2024

4 Semester

4

Students should learn the basic concepts and methods of complex analysis, complex numbers, basic operations on complex numbers, residues theory, application of residues theory to the calculation of integrals, students should be able to solve typical problems requiring the use of complex numbers, calculate integrals by complex analysis, calculate residues, find the integrals with the help of residues.

Full-time form

For studying the discipline "Special topics of higher mathematics" it is necessary to have basic knowledge of mathematics and the course "Higher Mathematics".

The basic normative discipline "Special topics of higher mathematics" consists of the following main sections: "Functions of a complex variable" and "Residues theory". These sections include such basic concepts as complex numbers and basic operations on complex numbers, the derivative of the function of a complex variable, analytical functions, the integral of the function of a complex variable, residues and their appli-cations. All mathematical concepts studied are illustrated by applications. When studying the course, both final tests and individual independent work of students are provided.

[1] Є. Д. Бiлоколос, Д. Д. Шека, Збiрник задач з математичної фізики. Київ — 2020. – 75 с. [2] Юрачківський А.П., Жугаєвич А.Я. Математична фізика в прикладах і задачах. – К: ВПЦ «Київський університет», – 2005. – 157 с.

Lectures - 30 hrs, practical lessons - 30 hrs, independent work - 40 hrs, total - 100 hrs.

- semester control: it is planned to conduct two written tests on the material of practical classes (MKR-1, MKR-2). A maximum of 25 points is awarded for each modular test. Activity in practical classes is estimated at a maximum of 10 points. According to the results of the semester control, a student can receive up to 60 points. - final control (in the form of an exam): the form of the exam is written-oral. In total, you can get from 0 to 40 points for the exam. The condition for achieving a positive grade for the discipline is to obtain at least 60 points, the grade for the exam can not be less than 20 points.

Ukrainian