Elementare partielle Differenzialgleichungen
The course Elementare partielle Differenzialgleichungen will take place in the summer semester 2022.
The course is designed to familiarise undergraduate students with the fascinating field of partial differential equations (PDEs).
Many processes and phenomena in the sciences, like e.g. diffusion, transport, waves, vibrations, fluid flow, electrodynamics, can be described by means of PDEs. They also play an important role in mathematical finance, e.g. in the Black-Scholes option pricing model.
The characteristic difference to an ordinary differential equation is that the unknown function depends on several variables and that partial derivatives with respect to different variables appear in the equation. For example, one might have several space variables or a time and at least one spatial variable.
Organization of the course
This course is a 4 ECTS course consisting of two lecture hours and one exercise session each week.
The course takes place in presence. The lecture is on Wednesdays at 10:15 am in N24, Room 226 and the exercise is on Fridays at 10:15 am in N24, Room 131.
If all participants agree we can change the course language from English to German.
Please register in Moodle for the course.
We will study important examples of PDEs by means of classical methods. Previous knowledge in functional analysis is not required. ODEs (ordinary differential equations) are desired but not necessarily required. It is possible to follow this course parallel to the course on ODEs.
- L. Evans: Partial Differential Equations, American Mathematical Society (excellent book!)
- B. Schweizer: Partielle Differentialgleichungen: Eine anwendungsorientierte Einführung, Springer
- M. Renardy, R. Rogers: An Introduction to Partial Differential Equations, Springer
- F. Sauvigny, Partielle Differentialgleichungen der Geometrie und der Physik, Springer
- J. Jost, Partielle Differentialgleichungen, Springer
- S. Salsa: Partial Differential Equations in Action, Springer
- W. Arendt, K. Urban: Partielle Differenzialgleichungen, Springer