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Functional Analysis
Major: System Analysis
Code of subject: 6.124.00.O.064
Credits: 3.00
Department: Mathematics
Lecturer: Sc.D ., Prof. Petro Kalenyuk
Semester: 5 семестр
Mode of study: денна
Learning outcomes: As a result of studying the discipline, the student must:
a) to know the basic modern methods of functional analysis;
b) be able to apply these methods to the solution of specific applications
tasks, including:
• to check the axioms of metric, norm, scalar product;
• apply contraction mapping principle;
• 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, Differential equations.
Summary of the subject: Metric spaces. The principle of compression mapping. Linear spaces. Linear normed spaces. Banach spaces. Spaces with a scalar product. Hilbert spaces. Linear functional and linear operators in Hilbert spaces.
Assessment methods and criteria: • Current control (30 point): oral examination in practical classes, two written tests
• Final control (70 point, credit ): testing (70 point)
• Total for discipline: 100 point
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.