Mathematical Analysis
Course:
Structural unit: Faculty of Physics
Title
Mathematical 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
3 Semester
Number of ECTS credits allocated
3
Learning outcomes
Students' knowledge of basic definitions, concepts, results and methods of classical theory of number and function series, proper and improper integrals with parameters, Fourier analysis. Students' ability to apply basic concepts and methods of mathematical analysis to solving problems in physics and astronomy. Students’ teamwork experience and improvement of the acquired communicative skills in professional activity. Students’ ability to independently and timely perform tasks, analyze solutions and be responsible for the results of their activities.
Form of study
Prerequisites and co-requisites
Elementary mathematics (algebra, geometry),
material of the 1st and 2nd semesters.
Course content
Family of functions. Number and function series. Power series. Integrals with parameters. Trigonometric Fourier series. Fourier integral and transform. Fourier series in Euclidean space.
Recommended or required reading and other learning resources/tools
1. Lyashko І. І., Yemelyanov V. F., Boyarchuk O. K. Mathemetical analysis, part 1 . – К.: Vyshcha shkola, 1992. – 495 p. (In Ukrainian).
2. Lyashko І. І., Yemelyanov V. F., Boyarchuk O. K. Mathemetical analysis, part 2 . – К.: Vyshcha shkola, 1993. – 375 p. (In Ukrainian).
3. Dorohovtsev А. Ya. Mathematical analysis, part 1. – К.: Lybid, 1993. – 320 p. (In Ukrainian).
4. Dorohovtsev А. Ya. Mathematical analysis, part 1. – К.: Lybid, 1994. – 302 p. (In Ukrainian).
5. Demidovich B. P. Collection of tasks and exercises on mathematical analysis. – M.: Nauka, 1990. – 524 p. (In Russian).
6. Kryvosheya S. А., Mayko N. V., Motorna О. V., Proshchenko Т. М. Mathematical analysis. Assignments for students’ independent work. Part 2: Tutorial. – К: Publishing and printing center "Kyivskyi universytet", 2015. – 350 p. (In Ukrainian).
Planned learning activities and teaching methods
Lectures – 14 hrs, practical lessons – 28 hrs, independent work – 47 hrs, consultations – 1 hr,
total – 90 hrs.
Assessment methods and criteria
Knowledge and skills evaluation: 100-point scale.
Current control (60 points): individual assignments, writing tests, colloquiums.
Final control at the end of each semester (40 points): writing tests.
Language of instruction
Ukrainian
Lecturers
This discipline is taught by the following teachers
Departments
The following departments are involved in teaching the above discipline