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1 |
Name of course |
Complex analysis |
|
2 |
Year |
2, Speciality Mechanics and Mathematical Modelling |
|
3 |
Semester |
4 |
|
4 |
Credits |
4 |
|
5 |
Lecturer’s scientific and academic degree, First Name, Patronic Name, Surname |
Doctor of Sciences (habilitated), Professor Edmund Ivanavič Zviarovič |
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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 complex analysis and its possibilities in modern scientific models. Skills forming of applying complex analysis for constructing and research of mathematical models. At the end of the course a student will be able: – to use main results of complex analysis in practice; – to use theoretical and practical skills of the complex variable function theory in mathematics. |
|
7 |
Background |
Algebra and numbers theory, Analytical Geometry, Mathematical Analysis. |
|
8 |
Contents |
Introduction to complex analysis. Differentiability of functions of a complex variable. Elementary analytical functions. Integration of complex-valued functions. Sequences and series of analytical functions. Laurent series and isolated singularities. The calculus of residues and its application. Laplace transform and operational calculus. Asymptotic series. |
|
9 |
Bibliography |
1.Б.В. Шабат. Введение в комплексный анализ. Ч. I. М.: Наука, 1976. 2.И.А. Александров, В.В. Соболев. Аналитические функции комплексного переменного. М.: Высшая школа, 1984. 3. М.А. Лаврентьев, Б.В. Шабат. Методы теории функций комплексного переменного. М.: Наука, 1973. 4. Л.И. Волковысский, Г.Л. Лунц, И.Г. Араманович. Сборник задач по теории функций комплексного переменного. М.: Наука, 1970. 5.Сборник задач по теории аналитических функций / Под ред. М.А. Евграфова, М., 1972. 6. Э.И. Зверович. Вещественный и комплексный анализ. Т. 1-6. Минск: Вышэйшая школа, 2008. 7. Ю.В. Сидоров, М.Ф. Федорюк, М.И. Шабунин. Лекции по ТФКП. М.: Наука, 1989. |
|
10 |
Methods of teaching |
Comparative method, problematic method, dialog and heuristic method, method of forming knowledge of a personal significance. |
|
11 |
Language |
English |
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12 |
Requirements, monitoring |
–estimation of individual student works; – oral test; –class test work. |
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13 |
Form of assessment |
Test |