Kathrin Eisenschmidt is a Ph.D. student at the Institute of Aerospace Thermodynamics, University Stuttgart. The three-lecture, introductory course to analytical methods for partial differential equations is aimed (not exclusively) at master's students of technical universities.

Abstract: An introduction to linear partial differential equations is given in this course.
Partial differential equations describe most of the problems in thermodynamics and fluid mechanics. Examples are the Navier-Stokes equation and the energy equation. These equations can be solved only numerically for general cases. Nevertheless, analytical solutions of problems in the field of thermodynamics and fluid mechanics are still of great importance. They help us to understand the basic principles of these problems and allow the estimation of the influence of single parameters on the solution, or the evaluation of results of numerical simulations. Analytical solutions are also of great relevance as a benchmark during the development of numerical solvers.
A method to solve linear partial differential equations is the separation of variables. This course focuses on that method. Examples like transient 1D heat conduction demonstrate the application of this method as well as more sophisticated problems like a flow through a duct with axial heat conduction.

More details: Tomáš Němec, ÚT AV ČR, nemec@it.cas.cz