Module MA5034-KP04, MA5034

Duration

1 Semester

Turnus of offer

every second summer semester

Credit points

4

Course of studies, specific fields and terms:

• Master MES 2020, optional subject, mathematics / natural sciences
• Master Medical Informatics 2019, optional subject, medical image processing
• Master MES 2014, optional subject, mathematics / natural sciences
• Bachelor CLS 2010, optional subject, mathematics
• Master Medical Informatics 2014, optional subject, medical image processing
• Master MES 2011, optional subject, mathematics
• Master Computer Science 2012, optional subject, advanced curriculum numerical image processing
• Master MES 2011, advanced curriculum, imaging systems, signal and image processing
• Master CLS 2010, optional subject, mathematics

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:

• Prof. Dr. rer. nat. Jan Modersitzki

Teacher:

• Institute of Mathematics and Image Computing
• Prof. Dr. rer. nat. Jan Modersitzki
• Prof. Dr. rer. nat. Jan Lellmann

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:

Last Updated:

14.12.2021