Winter Term 2020
The list of courses is available in German only.
Modellierung mit partiellen DifferentialgleichungenDr. Annette Miltenberger; Dr. Philipp Reutter; Univ.-Prof. Dr. Peter Spichtinger
Course No.: 08.079.791
Requirements / organisational issuesPrerequisites:
- Lectures Mathematics for Physicists or equivalent prior knowledge
- Modeling with ordinary differential equations helpful but not mandatory
Digitale LehreThe lecture will be held digitally, with recordings of the lecture posted online (asynchronous event). The exercise will be held in a synchronous digital form, where questions about the lecture as well as the exercise problems will be discussed.
ContentsIn this lecture an overview of modeling with partial differential equations is given. Based on many examples from the natural sciences (physics, chemistry, biology), important approaches to modeling are presented, including the analysis of the underlying equations. In addition to the theory and examples, numerical methods for solving the differential equations are also presented.
Specifically, the following contents are covered:
- Classification of linear partial differential equations
- modeling of simple problems (wave equation, heat conduction equation, Laplace equation)
- Analytical solution methods (method of characteristics, separation of variables, similarity approaches)
- Nonlinear problems (flows, reaction-diffusion equations)
- Numerical methods for the solution of partial differential equations (finite differences, finite elements, spectral methods)
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Semester: SoSe 2021