Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

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)