Courses

Current Courses in the Winter Term 2024/25

Course "Hyperbolic Conservation Laws"

  • Date: Wednesdays, 10:00 to 11:30 a.m. (the course starts on 23. October 2024)
  • Room: F 426
  • Exercise class: Thursdays, 11:45 to 13:15 in room D 404 (the first exercise class takes place on 07. November 2024)
  • Content: The course deals with an important class of partial differential equations, namely the hyperbolic conservation laws. We will discuss several notions of solutions, we will study existence and uniqueness, and we will solve simple initial value problems.
  • Recommended prerequisites: Analysis I-III; some knowledge in the theory of partial differential equations is helpful but not required.
  • Can be taken as a specialization module or as an elective module in the Master's programme, or within the "Spezielles Gebiet" in the Master of Education programme.

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Planned Topics:

  • Scalar conservation laws: method of characteristics, weak solution, entropy condition, Riemann problem, existence and uniqueness following Kruzkov
  • 1-D systems: weak solution, entropy condition, hyperbolicity, linear systems, non-linear system (by considering the example of the compressible Euler equations), Riemann problem
  • Mulit-D Euler equations (if time allows): short introduction to convex integration, measure-valued solutions

Past Courses

List of all courses I have taught

  • Summer term 2023: Course "Mathematical Continuum Mechanics", University of Würzburg
  • Michaelmas 2021: Supervision "Analysis and Topology", King's College, University of Cambridge
  • Summer term 2020: Exercise class "Analysis 2", University of Würzburg
  • Winter term 2019/20: Exercise class "Analysis 1", University of Würzburg
  • Summer term 2019: Exercise class "Lineare Algebra 1", University of Würzburg
  • Winter term 2018/19: Exercise class "Einführung in die partiellen Differentialgleichungen", University of Würzburg
  • Summer term 2018: Exercise class "Lineare Algebra 2", University of Würzburg
  • Winter term 2017/18: Exercise class "Lineare Algebra 1", University of Würzburg
  • Summer term 2017: Exercise class "Analysis 2", University of Würzburg

A more detailled teaching record can be found in my CV.