Course MAT-12-23-K-3
Introduction to Functional Analysis (2V+1U, 4.5 LP)
Course Type
| SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
|---|---|---|---|---|---|
| - | K | Lecture with exercise classes (V/U) | 4.5 CP | 93 h | |
| 2 | V | Lecture | 28 h | ||
| 1 | U | Exercise class (in small groups) | 14 h | ||
| (2V+1U) | 4.5 CP | 42 h | 93 h | ||
Basedata
| SWS | 2V+1U |
|---|---|
| CP, Effort | 4.5 CP = 135 h |
| Position of the semester | 1 Sem. in WiSe |
| Level | [3] Bachelor (Core) |
| Language | [DE] German |
| Lecturers |
+ further Lecturers of the department Mathematics
|
| Area of study | [MAT-GRU] Mathematics (B.Sc. year 1 and 2) |
| Livecycle-State | [NORM] Active |
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 83130 ("Exercise Class Introduction to Functional Analysis")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Contents
- examples of Banach and Hilbert spaces;
- compactness, Heine-Borel, Arzela-Ascoli;
- bounded linear operators, adjoint operators, Neumann series;
- orthogonality, basis of a Hilbert space, Riesz representation, Lax-Milgram, selfadjoint operators, spectral theory.
Competencies / intended learning achievements
The students are familiar with the basic concepts, statements and methods of functional analysis; in particular, they have been introduced to the theory of infinite-dimensional spaces. Thus, advanced abstraction skills have been promoted.
Literature
- H.W. Alt: Lineare Funktionalanalysis,
- H. Heuser: Funktionalanalysis.
Materials
Further literature will be announced in the lecture(s); exercise material is provided.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Modules:
Requirements for attendance (formal)
None
References to Course [MAT-12-23-K-3]
| Module | Name | Context | |
|---|---|---|---|
| [MAT-12-10P-M-3] | Build-Up Module Mathematics (for Students of Physics) | WP: Obligation to choose | 2V+1U, 5.0 LP |
| [MAT-12-20L_ERW-M-3] | Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation | WP: Obligation to choose | 2V+1U, 4.5 LP |
| [MAT-12-20L-M-3] | Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation | WP: Obligation to choose | 2V+1U, 4.5 LP |
| Course-Pool | Name | ||
| [MAT-10-KPOOL-3] | Pure Mathematics (B.Sc. Mathematics) | ||
| [PHY-M2-KPOOL-3] | Höhere Analysis (für Studierende der Physik) |