Every winter semester
10 Credit points
For information on the duration of the modul, refer to the courses of study in which the module is used.
Non-official translation of the module descriptions. Only the German version is legally binding.
Students are able to present the problems of volume measurement and integration in higher dimensions in a technically correct manner. They are able to implement intuitive geometric concepts - such as length and volume - in analysis and thus make them computationally accessible. Students develop an understanding of the fundamental principles of measurement and integration theory, which enables them to carry out mathematical proofs in this area independently. They can handle multidimensional integrals correctly and acquire basic knowledge and skills which they can apply in in-depth courses on functional analysis, probability theory, numerics and partial differential equations. They are confident in applying the methods of measure and integration theory and can successfully transfer these to new problems.
In the tutorials, students demonstrate the acquisition of competences in the technologies of measure and integration theory, the ability to apply the methods and conduct proofs under supervision, presentation and communication skills as well as perseverance as basic mathematical competences.
Understanding of the relationships and concepts, the ability to carry out proofs independently and confidence in applying the methods to new problems is demonstrated in the final exam.
- Introduction to the General Concept of Measure and Integral
- Construction of measures, in particular Lebesgue measure and Lebesgue integration
- Convergence theorems, Lp spaces, product measures, Fubini's theorem
- Integration in Rn, transformation theorem,
- Gauss's theorem.
Kompetenzen der fachlichen Basis in Analysis und Linearer Algebra (24-B-MG1, 24-B-MG2) sowie je nach gewählter Vorlesung weitere Kompetenzen
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Das Modul kann nicht zusammen mit dem Modul 24-B-MI-5 oder 24-B-MI studiert werden.
Module structure: 1 SL, 1 bPr 1
| Allocated examiner | Workload | LP2 |
|---|---|---|
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Teaching staff of the course
Tutorials for Analysis 3
(exercise)
Regular completion of the exercises, each with a recognisable solution approach, as well as participation in the exercise groups for the module's lecture. As a rule, participation in the exercise group includes presenting solutions to exercises twice after being asked to do so as well as regular contributions to the scientific discussion in the exercise group, for example in the form of comments and questions on the proposed solutions presented. The organiser may replace some of the exercises with face-to-face exercises. |
see above |
see above
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The (e-)portfolio is passed if
- a sufficient number of correctly solved exercises, which are completed as part of the study requirements , are demonstrated, usually by at least 50% of the points achievable in the semester for solving the exercises, and
- a final exam in the form of a final written exam (usually 90 min) or a final oral exam (usually 30 min) is passed. The final exam relates to the content of the lecture and the tutorial and is used for assessment.
An electronic written examination at a distance is not permitted as a final exam.
| Degree programme | Version | Recommended start 3 | Duration | Mandatory option 4 |
|---|---|---|---|---|
| Mathematics / Bachelor of Science [FsB vom 28.02.2025] | Major Subject (Academic) | 3. o. 4. | one semester | Obligation |
| Mathematics / Bachelor [FsB vom 28.02.2025] | Minor Subject (Academic), 60 CPs | 4. o. 5. o. 6. | one semester | Compulsory optional subject |
| Mathematics / Bachelor of Science [FsB vom 28.02.2025] | Major Subject (Advanced Secondary and Comprehensive Schools ('Gymnasium' and 'Gesamtschule')) | 3. o. 4. o. 5. o. 6. | one semester | Compulsory optional subject |
| Mathematical Economics / Bachelor of Science [FsB vom 28.02.2025 mit Berichtigung vom 30.04.2025] | Bachelor with One Core Subject (Academic) | 3. o. 4. | one semester | Obligation |
The system can perform an automatic check for completeness for this module.