Partial Differential Equations 2 - Variational Methods
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
MA5052 is a semester module in English language at Master’s level which is offered irregular.
This module description is valid from WS 2015/6 to SS 2018.
|Total workload||Contact hours||Credits (ECTS)|
|270 h||90 h||9 CP|
Content, Learning Outcome and Preconditions
Elements from the Calculus of Variations, Sobolev Spaces, elliptic and time dependent problems, variational inequalities, linear and nonlinear problems.
After successful completion of the module, students are able to apply variational techniques to a variety of linear and nonlinear partial differential equations.
MA1001 Analysis 1, MA1002 Analysis 2, MA2003 Measure and Integration Theory, MA3001 Functional Analysis, MA3005 Partial Differential Equations
Courses, Learning and Teaching Methods and Literature
Learning and Teaching Methods
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.
L.C. Evans, Partial Differential Equations, GSM 19 Am. Math. Soc. 1998.
Description of exams and course work
The module examination is based on a written exam (60-90 minutes). Students have to understand fundamental techniques and methods and particularly variational methods. They are able to apply them to a variety of linear and nonlinear partial differential equations.
The exam may be repeated at the end of the semester.