Group | Type | Day | Time | Classroom | Weeks | Comment |
---|---|---|---|---|---|---|
Common | I | Monday | 10-12 | U9 | 45-51 | |
Common | I | Thursday | 12-14 | U27 | 45-51 | |
S1 | TE | Monday | 12-14 | U131 | 46-51 | |
S1 | TE | Friday | 12-14 | U148 | 45-50 |
Ubegrænset deltagerantal
Prerequisites:
None
Academic preconditions:
The content of the courses MM501 Calculus I, MM502 Calculus II, MM505 Linear Algebra, MM508 Topology I, MM509 Topology II, and MM517 Measure and Integration Theory must be known.
Course introduction
To introduce Functional Analysis with special emphasis on Hilbert- and Banach Space Theory. This gives the basics for more advanced studies in modern Functional Analysis, in particular in Operator Algebra Theory and Banach Space Theory.
Expected learning outcome
At the end of the course the student will be able to:
-reproduce the definitions within the syllabus of the course in a precise mathematical language
- reproduce results, together with complete proofs, within the syllabus of the course
- relate the results within the syllabus of the course to each other
- apply the theory to solve problems within the scope of the syllabus of the course
- compute Fourier series and Fourier integrals of functions and predict their convergence properties based on regularity properties of the functions
- discuss the applications of functional analysis in the theory of differential equations
Subject overview
Hilbert spaces. Fourier series and Fourier integrals. Introduction to Banach Space Theory. The Banach-Steinhaus theorem. The open mapping theorem. The Hahn-Banach extension theorem. The representation theorem of Riesz for positive linear functionals on C(K).
Literature
Reexamination after 4th quarter.
Expected working hours
The teaching method is based on three phase model.
Forelæsninger: 28 timer
Eksaminatorietimer/opgaveregning: 21 timer
Educational activities
Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.
Course enrollment
See deadline of enrolment.
Tuition fees for single courses
See fees for single courses.