1

Name of course

Additional chapters of mathematical analysis

2

Year

2, Speciality

Mathematics (scientific- industrial activity)

3

Semester

4

4

Credits

6

5

Lecturer’s scientific and academic degree, First Name, Patronic Name, Surname

Doctor of Sciences (habilitated), Professor Venjamin  Ryhoravič Krotaŭ

6

Goals of course

Formation of a basic knowledge for understanding of principal concepts and methods of modern mathematics. Forming a basis of mathematical way of thinking, acquaintance of students with mathematical methods of constructing theorem proofs, studying algorithm of solving on particular mathematical problems.

At the end of the course a student will be able:

– to use main results of mathematical analysis in practice;

– to use theoretical and practical skills of differential and integral calculus in mathematics.

7

Background

Elementary mathematics, Algebra and numbers theory, Analytical Geometry, Mathematical Analysis (1-3 semesters).

8

Contents

Functions of bounded variation. Riemann-Stieltjes integral. Fourier series. Operations with series of constants. Space of continuous functions. Best approximations by trigonometric polynomials. Haar system. Convex functions. Lebesgue criterion of integrability of a function. Fourier transform. Stirling’s formula.

9

Bibliography

1. Г.И. Архипов, В.А. Садовничий, В.Н. Чубариков. Лекции по математическому анализу. М.: Высшая школа, 2000.

2. В.А. Зорич. Математический анализ (2 тома). М.: Наука, 1981 и другие издания.

3. В.А. Ильин, В.А. Садовничий, Б.Х. Сендов. Математический анализ. М.: Наука, 1979.

4. Л.Д. Кудрявцев. Курс математического анализа. М.: Высшая школа, Т. 1, 2. 1981 и другие издания.

5. С.М. Никольский. Курс математического анализа. Т. 1, 2. М.: Наука. 1990.

6. Б.П. Демидович. Сборник задач и упражнений по математическому анализу. М.: Наука, 1990.

7. Э.И. Зверович. Вещественный и комплексный анализ. Т. 1–6. Минск: Вышэйшая школа, 2008.

8. Сборник задач по математическому анализу /Под ред. Л.Д. Кудрявцева, М.: Наука, Т. 1. – 1984, Т. 2. – 1986, Т. 3 – 1994 и другие издания.

10

Methods of teaching

Comparative method, problematic method, dialog and heuristic method, method of forming knowledge of a personal significance.

11

Language

English

12

Requirements, monitoring

–estimation of individual student works;

– oral test;

–class test work;

Exam grade consists of

30 % – practical work in class, 10 % – oral test, 10 % –class test work;

50 % –answer on exam.

13

Form of assessment

Test, Exam