Operatorer på Hilbertrum

2018/2019

Modulets indhold, forløb og pædagogik

Læringsmål

Viden

  • are familiar with introductory functional analysis including completions, Banach spaces and Hilbert spaces
  • have acquired an understanding of orthonormal bases
  • have familiarity and understanding of bounded linear operators and their adjoints
  • are familiar with the closed graph and the open mapping theorems
  • are familiar with the spectral theory for bounded operators
  • know the spectral theorem for self-adjoint and compact operators

Færdigheder

  • are able to carry out proofs for central results within the theory of Banach and of Hilbert spaces
  • can apply theoretical results from the module to the analysis of examples

Kompetencer

  • are able to apply central results from mathematical analysis and from linear algebra in the investigation of linear operators on Hilbert space and their properties
  • are able independently to invoke results from functional analysis to the treatment of questions within related areas of mathematical analysis

Undervisningsform

Forelæsninger med tilhørende opgaveregning.



Omfang og forventet arbejdsindsats

Kursusmodulets omfang er 5 ECTS svarende til 150 timers studieindsats.

Eksamen

Prøver

Prøvens navnOperatorer på Hilbertrum
Prøveform
Skriftlig eller mundtlig
In order to participate in the exam, students must have actively participated in course progress by way of one or several independent oral and/or written contributions.
ECTS5
BedømmelsesformBestået/ikke bestået
CensurIntern prøve
VurderingskriterierSom angivet i Fællesbestemmelser for uddannelser (Vurderingskriterier).
http:/​/​www.engineering.aau.dk/​uddannelse/​Studieadministration/​

Fakta om modulet

Engelsk titelOperators on Hilbert Spaces
ModulkodeF-MAT-K2-5
ModultypeKursus
Varighed1 semester
SemesterForår
ECTS5
TompladsJa
UndervisningsstedCampus Aalborg
Modulansvarlig

Organisation

StudienævnStudienævnet for Matematik, Fysik og Nanoteknologi
FakultetDet Ingeniør- og Naturvidenskabelige Fakultet
SkoleSkolen for Ingeniør- og Naturvidenskab