Introduction to Functional Analysis (2V+1U, 4.5 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||4.5 CP||93 h|
|1||U||Exercise class (in small groups)||14 h|
|(2V+1U)||4.5 CP||42 h||93 h|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. in WiSe|
|Level|| Bachelor (Core)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-GRU] Mathematics (B.Sc. year 1 and 2)|
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.
- 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.
- H.W. Alt: Lineare Funktionalanalysis,
- H. Heuser: Funktionalanalysis.
Further literature will be announced in the lecture(s); exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Requirements for attendance (formal)None
References to Course [MAT-12-23-K-3]
|[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|
|[MAT-10-KPOOL-3]||Pure Mathematics (B.Sc. Mathematics)|
|[PHY-M2-KPOOL-3]||Höhere Analysis (für Studierende der Physik)|