Duration:
1 Semester | Turnus of offer:
every second summer semester | Credit points:
4 |
Course of studies, specific field and terms: - Master MES 2020 (optional subject), mathematics / natural sciences, Arbitrary semester
- Master Medical Informatics 2019 (optional subject), medical image processing, 1st or 2nd semester
- Master MES 2014 (optional subject), mathematics / natural sciences, Arbitrary semester
- Bachelor CLS 2010 (optional subject), mathematics, 4th or 6th semester
- Master Medical Informatics 2014 (optional subject), medical image processing, 1st or 2nd semester
- Master MES 2011 (optional subject), mathematics, 2nd or 4th semester
- Master Computer Science 2012 (optional subject), advanced curriculum numerical image processing, 2nd or 3rd semester
- Master MES 2011 (advanced curriculum), imaging systems, signal and image processing, 2nd or 4th semester
- Master CLS 2010 (optional subject), mathematics, 2nd or 4th semester
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Classes and lectures: - Calculus of Variations and Partial Differential Equations (exercise, 1 SWS)
- Calculus of Variations and Partial Differential Equations (lecture, 2 SWS)
| Workload: - 10 Hours exam preparation
- 45 Hours in-classroom work
- 65 Hours private studies and exercises
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Contents of teaching: | - Motivation and application examples
- Functional-analytic foundations
- Direct methods in the calculus of variations
- The dual space, weak convergence, Sobolev spaces
- Optimality conditions
- Classification of partial differential equations and typical PDEs
- Fundamental solutions, maximum principle
- Finite elements for elliptical partial differential equations
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Qualification-goals/Competencies: - Students understand variational modeling.
- They are able to formulate basic physical problems in a variational setting.
- They understand the connections between variational methods and partial differential equations.
- They can derive optimality conditions for energy functionals.
- They understand the mathematical theory behind selected variational problems.
- They can implement selected fundamental variational problems.
- They can formulate selected practical problems in the variational setting.
- Interdisciplinary qualifications:
- Students have advanced skills in modeling.
- They can translate theoretical concepts into practical solutions.
- They are experienced in implementation.
- They can think abstractly about practical problems.
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Grading through: - Written or oral exam as announced by the examiner
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Responsible for this module: Teachers: |
Literature: - Vogel: Computational Methods for Inverse Methods - SIAM
- Aubert, Kornprobst: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations - Springer
- Scherzer, Grasmair, Grossauer, Haltmeier, Lenzen: Variational Methods in Imaging - Springer
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Language: - German and English skills required
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Notes:Prerequisites for attending the module:
- None (Familiarity with the topics of the required modules is assumed, but the modules are not a formal prerequisite for attending the course).
Prerequisites for the exam:
- Preliminary examinations can be determined at the beginning of the semester. If preliminary work has been defined, it must have been completed and positively assessed before the first examination.
Examination:
- MA5034-L1: Calculus of Variations and Partial Differential Equations, written examination (90min) or oral examination (30min) as decided by examiner, 100% of final mark |
Letzte Änderung: 14.12.2021 |
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