Functional Analysis (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)|
|4||V||Lecture||6.0 CP||56 h||124 h|
|2||U||Exercise class (in small groups)||3.0 CP||28 h||62 h|
|(4V+2U)||9.0 CP||84 h||186 h|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. in SuSe|
|Level|| Bachelor (Specialization)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 84020 ("Exercise Class Functional Analysis")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
- Hahn-Banach theorem and its applications,
- Baire category theorem and its applications (uniform boundedness principle, Banach-Steinhaus-Theorem, open mapping theorem, inverse mapping theorem, closed graph theorem),
- Weak convergence (Banach-Alaoglu theorem, reflexive Banach spaces, Mazur lemma and its applications),
- Projections (closed complement theorem),
- Bounded operators (adjoint operator, spectrum, resolvent, normal operators),
- Compact operators (Fredholm operators, Fredholm alternative and its applications, spectral theorem(Riesz-Schauder) and its application to normal operators),
- Unbounded operators (graph, symmetric and self-adjoint operators).
Competencies / intended learning achievements
The students have studied and understand the mathematical concepts in infinite-dimensional spaces with a special emphasis on analytical aspects. They have gained the basic analytical tools required for solving differential and integral equations in theory and application.
- H.-W. Alt: Lineare Funktionalanalysis,
- H. Heuser: Funktionalanalysis,
- M. Reed, M, B. Simon: Functional Analysis I,
- D. Werner: Funktionalanalysis.
Further literature will be announced in the lecture; 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)
- [MAT-12-23-K-3] Introduction to Functional Analysis (2V+1U, 4.5 LP)
- [MAT-12-28-K-3] Measure and Integration Theory (2V+1U, 4.5 LP)
Requirements for attendance (formal)
References to Course [MAT-70-11-K-4]
|[MAT-30-10L-M-5]||Specialisation Module (Teachers Training Programme Mathematics)||WP: Obligation to choose in Obligatory-Modulteil #A (Lectures)||4V, 6.0 LP|
|[MAT-70-11-M-4]||Functional Analysis||P: Obligatory||4V+2U, 9.0 LP|
|[MAT-70-4V-KPOOL-4]||Elective Courses Analysis and Stochastics (4V, B.Sc.)|
|[MAT-70-KPOOL-4]||Specialisation Analysis and Stochastics (B.Sc.)|
|[MAT-80-4V-KPOOL-4]||Elective Courses Modelling and Scientific Computing (4V, B.Sc.)|