6 ECTS credits
180 h study time
Offer 1 with catalog number 1017287BNR for all students in the 2nd semester
at
a (B) Bachelor - advanced level.
- Semester
- 2nd semester
- Enrollment based on exam contract
- Impossible
- Grading method
- Grading (scale from 0 to 20)
- Can retake in second session
- Yes
- Enrollment Requirements
- Students who want to enroll for this course, must have passed or be enrolled for "Analyse en Topologie in metrische ruimten".
- Taught in
- Dutch
- Faculty
- Faculty of Sciences and Bioengineering Sciences
- Department
- Mathematics
- Educational team
- Kenny De Commer
(course titular)
- Activities and contact hours
-
26 contact hours Lecture
26 contact hours Seminar, Exercises or Practicals
- Course Content
1. Normed vector spaces
2. Banach spaces
3. Hilbert spaces
4. Bounded linear operators
5. Spectral theorem for compact self-adjoint operators
6. Fourier analysis for periodic functions
7. Fourier integrals
- Course material
- Digital course material (Recommended) : Inleiding tot de functionaalanalyse, Kenny De Commer
- Additional info
Notes will be supplied. Additional references will be given throughout the course.
- Learning Outcomes
-
General competences
To gain insight in the elementary theory of Banach- and Hilbert spaces and operators on them.
To be able to state and prove definitions and theorems from the course notes correctly. To comment on those writings orally. To be able to make links independantly and to answer questions requiring insight/open questions.
To be able to solve exercises similar to those treated during the tutorials and write up the answers in a correct and clear way.
- Grading
-
The final grade is composed based on the following categories:
Oral Exam determines 40% of the final mark.
Written Exam determines 60% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
- mondeling examen
with a relative weight of 40
which comprises 40% of the final mark.
Note: mondeling examen over de theorie
Within the Written Exam category, the following assignments need to be completed:
- schriftelijk examen
with a relative weight of 60
which comprises 60% of the final mark.
Note: schriftelijk examen oefeningen
- Additional info regarding evaluation
Oral examination (40%) on theoretical material covered (open questions), written examination on exercises (60%)
- Allowed unsatisfactory mark
- The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.
Academic context
This offer is part of the following study plans:
Bachelor of Physics and Astronomy: Default track (only offered in Dutch)
Bachelor of Mathematics and Data Science: Standaard traject (only offered in Dutch)