Functional Analysis
Informacje ogólne
| Kod przedmiotu: | 360-MS2-1AFa | Kod Erasmus / ISCED: |
11.103
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(0541) Matematyka
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| Nazwa przedmiotu: | Functional Analysis | ||
| Jednostka: | Wydział Matematyki | ||
| Grupy: | |||
| Punkty ECTS i inne: |
6.00  zobacz reguły punktacji |
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| Język prowadzenia: | angielski | ||
| Rodzaj przedmiotu: | obowiązkowe |
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| Założenia (opisowo): | Acquainting with the basics of the theory of Banach spaces and the theory of continuous linear operators. |
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| Skrócony opis: |
Normed spaces. Banach spaces, completion, subspaces, quotient spaces. Classic Banach spaces. Bounded operators, the dual space. Hilbert spaces. Orthogonal projection - existence and uniqueness. Theorem on the form of a linear and bounded functional on a Hilbert space. Orthogonal basis. Hilbert space dimension. Operators in Hilbert spaces, adjoint operators, classes of operators. Hahn-Banach theorem, reflexive spaces. Dual spaces to classic Banach spaces. Banach-Steinhaus theorem and Baire theorem. Banach theorem on an open mapping. Closed graph theorem. Elements of spectral theory. |
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| Pełny opis: |
Educational profile: general academic Form of studies: full-time Compulsory subject Field: mathematical sciences, discipline: mathematics Year of study: 1, semester: 2 Pre-props: none lecture 30 hours exercises 30 hours Didactic methods: lectures, calculating exercises, consultations, work on literature, solving homework, discussions in problem groups. ECTS credits: 6 Balance of student workload: participation in lectures15x2h = 30h participation in exercises 15x2h = 30h preparation for classes 15x2h = 30h completing solving tasks started during the exercises and preparing notes at home after the classes (lectures, exercises) 7x2h = 14h participation in consultations 7x3h = 21h preparation for tests and participation in them 6 + 3x4h = 18h preparation for the exam and participation in it 12h + 3h = 15h Quantitative indicators student workload related to classes requiring the direct participation of an academic teacher: 84 hours, 3 ECTS student workload related to practical classes: 104 hours, 3 ECTS |
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| Literatura: |
J. B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, 1985. |
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| Efekty uczenia się: |
Student understands the concepts of Banach spaces and Hilbert spaces as well as basic facts and theorems related to them. Student knows the basics of the theory of continuous linear operators Student knows examples of bounded linear operators. KA7_WG01,KA7_WG02, KA7_WG03, KA7_WG04, KA7_UW02, KA7_UW03, KA7_UW04, KA7_UW08, KA7_UW0 |
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Zajęcia w cyklu "Rok akademicki 2022/23" (jeszcze nie rozpoczęty)
| Okres: | 2022-10-01 - 2023-06-30 |
 
 zobacz plan zajęć |
| Typ zajęć: |
Ćwiczenia, 30 godzin więcej informacji Wykład, 30 godzin więcej informacji |
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| Koordynatorzy: | Tomasz Czyżycki, Bartosz Kwaśniewski, Aneta Sliżewska | |
| Prowadzący grup: | (brak danych) | |
| Lista studentów: | (nie masz dostępu) | |
| Zaliczenie: | Egzamin |
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.