Module Number:
| 13844
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Module Title: | Functional Analysis |
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Funktionalanalysis
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Department: |
Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
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Responsible Staff Member: | -
Prof. Dr. rer. nat. habil. Wachsmuth, Gerd
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Language of Teaching / Examination: | English |
Duration: | 1 semester |
Frequency of Offer: |
On special announcement
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Credits: |
8
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Learning Outcome: | The students have
- expanded and intensified their knowledge from previous modules of Analysis and Algebra
- competently mastered definitions and interrelations within abstract spaces
- become acquainted with applications in Numerics, Optimization, and Physics
- acquired basic knowledge for advanced modules
- became familiar with fundamental techniques of proof
- improved their logical way of thinking by solving problems in abstract spaces
- further developed their abilities for independent scientific work by treating themes from Functional Analysis
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Contents: | - Normed spaces
completion, separable spaces, Lebesgue spaces, spaces of continuous and differentiable functions, Sobolev spaces - Linear and continuous operators
Projection and adjoint operators, topological dual spaces, completely continuous operators, weak convergence and reflexivity - Main theorems
Weierstrass, Hahn-Banach, Schauder, the openmapping, the closed graph - Hilbert spaces
Spectral theorem for selfadjoint, completely continuous operators
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Recommended Prerequisites: | Knowledge of the content of the modules
- 11103 Analysis I
- 11104 Analysis II
- 11201 Analysis III
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Mandatory Prerequisites: | No successful participation in module 11303 - Funktionalanalysis. |
Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
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Exercise
/ 2 Hours per Week per Semester
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Self organised studies
/ 150 Hours
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Teaching Materials and Literature: | - Aubin, J.-P.: Applied Functional Analysis, Wiley, 2000, https://doi.org/10.1002/9781118032725
- Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011, https://doi.org/10.1007/978-0-387-70914-7
- Rudin, W.: Functional Analysis, McGraw Hill, 1991
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Module Examination: | Prerequisite + Final Module Examination (MAP) |
Assessment Mode for Module Examination: | Prerequisite:
- Successful completion of homework
Final module examination:
- Written examination, 90 min. OR
- Oral examination, 30 min. (with small number of participants)
In the first lecture it will introduced, if the examination will organized in written or oral form. |
Evaluation of Module Examination: | Performance Verification – graded |
Limited Number of Participants: | None |
Part of the Study Programme: | -
Master (research-oriented) /
Angewandte Mathematik /
PO 2019
- 1. SÄ 2021
-
Master (research-oriented) /
Artificial Intelligence /
PO 2022
- 1. SÄ 2024
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Bachelor (research-oriented) /
Mathematik /
PO 2023
-
Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Mathematik - dual /
PO 2023
-
Master (research-oriented) /
Physics /
PO 2021
-
Bachelor (research-oriented) /
Physik /
PO 2021
-
Bachelor (research-oriented) /
Wirtschaftsmathematik /
PO 2023
-
Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Wirtschaftsmathematik - dual /
PO 2023
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Remarks: | - Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Analysis / Algebra / Kombinatorik“
- Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
- Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
- Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
- Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Advanded Methods“
If there is no need that the module is taught in English, alternatively the german version 11303 „Funktionalanalysis“ may beread instead. |
Module Components: | - Lecture: Functional Analysis
- Accompanying exercises
- Related examination
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Components to be offered in the Current Semester: | |