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Regular version of the site
Master 2019/2020

## Selected Sections of Mathematics

Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Area of studies: Applied Mathematics
When: 1 year, 1, 2 module
Mode of studies: offline
Instructors: Sergey Artamonov
Master’s programme: Supercomputer Simulations in Science and Engineering
Language: English
ECTS credits: 4

### Course Syllabus

#### Abstract

This discipline belongs to the class of adaptation. The purpose of studying the discipline is to form students' basic knowledge in the field of Fourier analysis and the ability to apply fundamental principles to solve practical problems.

#### Learning Objectives

• As a result of studying the discipline, the student will know: 1. Fundamental provisions of selected sections of higher mathematics. 2. The main results of the theory of Hilbert spaces and Fourier analysis.
• be able to: 1. Use the main provisions of the selected sections of Fourier analysis for solving problems of mathematical physics. 2. Use the main provisions of selected sections of Fourier analysis for solving problems of approximation theory.
• have skills: 1. Solving model problems in selected sections of Fourier analysis and approximation theory. 2. Using the main provisions of the selected sections of Fourier analysis for solving problems of approximation theory.

#### Expected Learning Outcomes

• be able to: Use the main provisions of the selected sections of Fourier analysis for solving problems of mathematical physics. have skills: Solving model problems in selected sections of Fourier analysis and approximation theory.
• be able to: Use the main provisions of selected sections of Fourier analysis for solving problems of approximation theory. have skills: Using the main provisions of the selected sections of Fourier analysis for solving problems of approximation theory.

#### Course Contents

• Metric and normalized spaces. Continuous functions. Full spaces. The principle of compressing mappings and its application. Banach and Hilbert spaces. Examples: Lp spaces.
• Fourier series. Some problems of mathematical physics. Generalized functions and Fourier transform. Poisson summation formula. The main provisions of the theory of approximation.

#### Assessment Elements

• аудиторные занятия
• самостоятельные
• экзамен
• Контрольно-измерительные материалы

#### Interim Assessment

• Interim assessment (2 module)
0.25 * аудиторные занятия + 0.25 * самостоятельные + 0.5 * экзамен

#### Recommended Core Bibliography

• Элементы теории функций и функционального анализа : Учебник, Колмогоров А. Н., Фомин С. В., 1976

#### Recommended Additional Bibliography

• Linear algebra : concepts and methods, Anthony M., Harvey M., 2012