| Course Unit Code | 470-4111/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. |
| VOD03 | doc. Mgr. Petr Vodstrčil, Ph.D. |
| Summary |
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| Within the course the students will be introduced in fundamental notions of functional analysis, which is a subject unifying results and methods of many classical mathematical disciplines (algebra, geometry, calculus). It identifies and emphasizes what they have in common and, further, it generalizes them. Functional analysis is involved in various parts of mathematics and its applications and it provides tools enabling to formulate as well as solve complex practical problems. The introduced abstract notions will be demonstrated at examples and applications. |
| Learning Outcomes of the Course Unit |
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| The course aims at introducing the students in fundamentals of functional analysis. In order to solve a number of technical problems, it is necesarry to master this (rather technical) discipline. |
| Course Contents |
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Metric Space.
Complete Metric Space.
Banach Fixed Point Theorem.
Banach Space.
Linear Functionals.
Weak Convergence .
Hilbert Space.
Riesz Theorem.
Operators in Banach and Hilbert Spaces
Gateaux Derivative.
Fréchet Derivative.
Local and Global Extremes.
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| Recommended or Required Reading |
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| Required Reading: |
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| E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995. |
| J. Bouchala: Úvod do funkcionální analýzy, http://www.am.vsb.cz/bouchala. |
| Recommended Reading: |
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| E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995. |
P. Drábek, A. Kufner: Úvod do funkcionální analýzy, ZČU Plzeň, 1993.
P. Drábek, A. Kufner: Funkcionální analýza, ZČU Plzeň, 1994.
J. Lukeš: Zápisky z funkcionální analýzy, Karolinum, Praha, 1998.
L. Mišík: Funcionálna analýza, Alfa, Bratislava, 1989.
A. E. Taylor: Úvod do funkcionální analýzy, Academia, Praha, 1973.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 30 | 15 |
| Examination | Examination | 70 | 21 |