Partial Differential Equations
This Module is offered by TUM Department of Mathematics.
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
Module version of SS 2019 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
MA3005 is a semester module
in English language
at Master’s level
which is offered in winter semester.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
- Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
|Total workload||Contact hours||Credits (ECTS)|
Basic examples of elliptic, parabolic and hyperbolic problems; elementary solution methods; weak solutions; variational methods, including Dirichlet's principle; operator approach
After successful completion of the module students are able to understand, apply and analyze basic methods to treat partial differential equations. In particular they distinguish different types of partial differential equation and understand their basic properties. The students understand the concepts of classical and weak (variational) solutions to elliptic partial differential equations including the questions on existence, uniqueness and well-posedness as well as on regularity of solutions. Moreover, they can analyze structural properties of such solutions, i.e. by applying maximum principles.
MA1001 Analysis 1, MA1002 Analysis 2, MA2003 Measure and Integration, MA2004 Vector Analysis
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2, MA0003 Analysis 3
Courses and Schedule
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, Graduate Studies in Mathematics Vol. 19, AMS, 1998.
Description of exams and course work
The module examination is based on a written exam (90 minutes). Students have to know theoretical concepts and methods to solve partial differential equations and can apply and analyze them under time pressure.
The exam may be repeated at the end of the semester.