1

Name of course

Integral Equations

2

Year

3, Speciality

Mechanics and Mathematical Modelling

3

Semester

7

4

Credits

2

5

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

Senior Instructor

Natalia Iharaŭna Karpovič

6

Goals of course

Bring students up to high standard of professional competence and to form a concept about technical possibilities of this part of modern analysis. Description of basics of integral equations and its possibilities in modern scientific models. Skills forming of applying the integral equations theory for constructing and research of mathematical models.

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

– to solve problems with integral equations;

 ‑ to prove principal theorems about properties of integral equations;

– to construct resolvent function for Fredholm and Volterra equations;

– to use main results the integral equations calculus in practice;

– to use theoretical and practical skills of basics of the calculus in mathematics.

7

Background

Mathematical Analysis, Functional Analysis, Algebra and number theory.

8

Contents

Preliminaries. Fredholm integral equations of second type. Fredholm integral equations with symmetrical kernels. Abel and Volterra integral equations.

9

Bibliography

1.Васильева, А.Б. Интегральные уравнения / А.Б. Васильева, Н.А. Тихонов. – 2-е изд. – М. : ФИЗМАТЛИТ, 2002. – 160 с.

2.Ворошилов, А.А. Интегральные уравнения : практикум для студентов мех.-мат. фак. спец. 1-31 03 02 «Механика» / А.А. Ворошилов. – Минск : БГУ, 2011. – 65 с.

3.Дифференциальные и интегральные уравнения, вариационное исчисление в примерах и задачах / А.Б. Васильева [и др.] : под ред. И.Л. Легостаевой. – М.: ФИЗМАТЛИТ, 2003 – 432 с.

4.Интегральные уравнения / П.П. Забрейко [и др.] ; редкол.: В.М. Гринберг [и др.] – М. : Наука, 1968. – 448 с.

5.Килбас, А.А. Интегральные уравнения : курс лекций / А.А. Килбас. – Мн. : БГУ, 2005. – 143 с.

6.Краснов, М.Л. Интегральные уравнения: Задачи и примеры с подробными решениями / М.Л. Краснов, А.И. Киселев, Г.И. Макаренко. – М.: Ком.Книга, 2007. – 192 с.

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.

13

Form of assessment

Test