| Course title | Introduction to Functional Analysis |
|---|---|
| Course code | UMB/580 |
| Organizational form of instruction | Lecture |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the winter semester. |
| Semester | Winter |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | Compulsory |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
|---|
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| Course content |
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Sigma algebra, introduction of a Lebesgue measure, measurable sets, measurable functions. Definition of the Lebesgue integral - fundamental properties. Convergence theorems. Metric spaces, normed linear spaces, Banach and Hilbert spaces. Spaces of smooth functions, Lp spaces. Linear operators, continuous operators.
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| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Demonstration
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| Learning outcomes |
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Students should acquaint themselves with Lebesgue integral and basic functional spaces.
We introduce sigma algebra, outer measure and then Lebesgue measure, measure sets and functions. We define Lebesgue integral and show its basic properties. We work with metric spaces, normed spaces, in particular Banach and Hilbert spaces. As examples we will use spaces of smooth functions, Lp spaces and Sobolev spaces. We will study linear and continuous operators and their properties. We show a power and application of fixed point theorems. |
| Prerequisites |
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We assume knowledge of differentail and integral calculus (UMB/564, UMB/565, UMB/566) and Linear algebra UMB/551. It is better to pass before also Linear algebra II UMB/585, where similar topics is studied in spaces of finite dimension.
UMB/CV566 ----- or ----- UMB/CV585 ----- or ----- UMB/566 ----- or ----- UMB/566K ----- or ----- UMB/585 |
| Assessment methods and criteria |
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Oral examination
Active participation on practicals, solving of simple homeworks. Final oral exam. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics (2010) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Winter |