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Functional Analysis
Major: Applied mathematics and computer science
Code of subject: 6.113.00.O.053
Credits: 5.00
Department: Applied Mathematics
Lecturer: Sc. D., Prof., Petro Kalenyuk
Semester: 4 семестр
Mode of study: денна
Learning outcomes: to know: basic concepts, definitions and terms of the theory of measure, measurable functions and Lebesgue integral, metric, linear, normalized, Banach and Hilbert spaces, theory of linear functionals and linear operators; modern methods of functional analysis;
to be able: apply these concepts and methods to the solution of applied problems, in particular, concerning the dimension and integrability of functions, the calculation of element norms in different Banach spaces, and the norms of functionals and operators; use different concepts of convergence when solving problems; find the conjugate operator, the spectrum of the operator;
to have an idea: on the application of the concepts of functional analysis in various fields of knowledge, as well as in the disciplines of preparation of their professional direction.
Required prior and related subjects: Prerequisites: Mathematical analysis, Differential equations, Algebra and geometry;
Corequisites: Mathematical physics equations, Numerical methods part 2, Control theory.
Summary of the subject: The course "Functional Analysis" consists of sections: Section 1. Metric Spaces, Section 2. Measure theory and Lebesgue integral, Section 3. Linear normed spaces, Section 4. Hilbert spaces, Section 5. Linear functionals. Conjugate spaces, Section 6. Linear operators.
Assessment methods and criteria: Current control: practical classes, test work, two control works (40 %);
Final control: (60%): examination in writing form.
Recommended books: 1. Колмогоров А.М., Фомін С.В. Елементи теорії функцій і функціонального аналізу. – К.:Вища школа, 1974.
2. Березанский Ю.М., Ус Г.Ф., Шефтель З.Г. Функциональный анализ. – К.:Вища школа, 1990.
3. Треногин В.А. Функциональный анализ. – М.: Физматлит, 2002.
4. Люстерник Л.А., Соболев В.И. Краткий курс функционального анализа. – М.: Высш. Школа, 1982.
5. Дороговцев А.Я. Математичний аналіз. Ч. 2. – К.: Либідь, 1994.
6. Кадець В.М. Курс функціонального аналізу та теорії міри. – Львів: Видавець І.Е.Чижиков, 2012.
7. Городецкий В.В., Нагнибида Н.И., Настасиев П.П. Методы решения задач по функциональному анализу. - К.:Вища школа, 1990,
8. Треногин В.А., Писаревский Б.М., Соболева Т.С. Задачи и упражнения по функциональному анализу. - М.: Физматлит, 2002.
Functional Analysis
Major: Applied mathematics and computer science
Code of subject: 6.113.00.O.052
Credits: 5.00
Department: Mathematics
Lecturer: Kaleniuk Petro Ivanovich
Semester: 4 семестр
Mode of study: денна
Learning outcomes: As a result of studying the discipline students should be able to:
1) know the basic modern methods of functional analysis,
2) be able to apply these methods to such tasks as:
to check the axioms of metric, norm, scalar product;
apply compression mapping principles;
orthogonalise the systems of independent elements and build Fourier series;
check operators for linearity and boundedness;
find the spectrum of the operator.
Required prior and related subjects: Linear Algebra and Analytical Geometry, Mathematical Analysis.
Summary of the subject: Metric spaces. The principle of compression mapping. Linear spaces. Linear normalized spaces. Banach spaces. Spaces with a scalar product. Hilbert spaces. Linear functionals and linear operators in Hilbert spaces.
Assessment methods and criteria: Current control (20%): oral examination in practical classes, written tests
Final control (80%, credit): testing (20%)
Recommended books: Колмогоров А.М., Фомін С.В. Елементи теорії функцій і функціонального аналізу.--К.:Вища школа, 1974.
Кадець В.М. Курс функціонального аналізу та теорії міри. – Львів: Видавець І.Е.Чижиков, 2012.
Треногин В.А. Функциональный анализ.--М.: Физматлит, 2002.
Дороговцев А.Я. Математичний аналіз. Ч. 2. – К.: Либідь, 1994.
Треногин В.А., Писаревский Б.М., Соболева Т.С. Задачи и упражнения по функциональному анализу. -- М.: Физматлит, 2002.
Городецкий В.В., Нагнибида Н.И., Настасиев П.П. Методы решения задач по функциональному анализу. - К.:Вища школа, 1990