Elementare partielle Differenzialgleichungen
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
The course will take place completely online. Several teaching materials will be provided. For each single lecture, a script will be available at the scheduled time of the lecture (Monday, 14-16). We are also preparing various videos, which are intended to provide additional explanations and illustrations of important topics or to give summaries at the end of a chapter etc.
We will upload an exercise sheet (or a quiz) every week on Wednesday. The first exercise sheet will be available on Wednesday 21/04/2021. In order to achieve the 'Studienleistung', that is, to qualify for the exam, you should reach, in total, at least 50 percent of the points of all exercise sheets and quizzes. We will provide detailed solutions of the exercise problems every week. Concerning the grading of the exercises we will use the 'Votiersystem'. We intend to occasionally replace the exercise sheet by a quiz.
We are also organizing an online discussion platform via Zoom, see the virtual classroom. There will be a meeting every three to four weeks. Concerning questions and comments on the content of the course, participants can also use the corresponding forum.
The exam will be in oral form (approx. 30 min).
If all participants agree we can change the course language from English to German.
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