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Module guide

Module MA5034-KP04, MA5034

Calculus of Variations and Partial Differential Equations (VariPDE)

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
  • 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
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
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
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.
Grading through:
  • Written or oral exam as announced by the examiner
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
Language:
  • German and English skills required
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