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Faculty of Mathematics, Physics and Computer Sciences

Chair of Applied and Numerical Analysis – Prof. Dr. Holger Wendland

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Teaching

Courses

Number Sem. Hours Type Name Lecturer

Future lectures/courses (tentative list)

Semestertopic
  
WS 2022/23    
  • Applied functional Analysis (4+2)
  • High-dimensional Approximation (2+1)        
  • Oberseminar
SS 2023
  • Einführung in die höhere Analysis (3+2)
  • Einführung in die iterativen Methoden (3+2)
  • Oberseminar
WS 2023/24
  • Numerik der partiellen Differentialgleichung (4+2)
SS 2024
  • Grundlagen der Mathematik für Physiker II (4+2)
  • Uncertainty Quantification (2+1)
  • Oberseminar
  • Hauptseminar
WS 2024/25
  • Analysis I (4+2)
  • Oberseminar
SS 2025
  • Analysis II (4+2)
  • Oberseminar
WS 2025/26
  • Vektoranalysis (2+1)
  • Oberseminar
SS 2026
  • Einführung in die höhere Analysis (3+2)
  • Oberseminar


Bachelor/Master Theses

I am offering Bachelor and Master theses from the area of applied and numerical analysis. Currently, they are mainly concerned with one of the following topics:

  • Multivariate and high-dimensional approximation theory; particularly kernel-based methods and neural networks.
  • Meshfree methods for the solution of partial differential equations; particularly radial basis functions and particle methods.
  • Application of the methods mentioned above to problems from uncertainty quantification.

Some of the topics mentioned above are described in more detail on our research web page. In general, I am also open for own suggestions, as long as they are interesting and thematically not too far away from my own the research interests.

Required or suggested courses for a Bachelor thesis:

  • Einführung in die numerische Mathematik
  • Einführung in die höhere Analysis
  • Einführung in die iterativen Verfahren
  • Constructive approximation methods
  • Applied functional analysis

Required or suggested courses for a Master thesis:

  • Constructive approximation theory
  • Applied functional analysis
  • Numerics of partial differential equations
  • Meshfree methods
  • High-dimensional approximation
  • Uncertainty quantification

Examples of previous theses:

  • Operatortheortische Untersuchung kernbasierter Approximationsräume (Master)
  • Fehlerabschätzungen für regelarisierte, kernbasierte Approximationsverfahren in höhendimensionalen Räumen (Master)
  • Vergleich von Neuronalen Netzen und kernbasierten Verfahren zum Einfärben von Bildern (Bachelor)
  • Über kernbasierte Lernverfahren und neuronale Netze (Bachelor)
  • Ein gitterfreies Verfahren zur numerischen Lösung von Problemen der optimalen Steuerung partieller Differentialgleichungen (Master)
  • Kernel-based reconstruction for parametric partial differential equations (Master)
  • Approximative Berechnung der Helmholtz-Hodge Zerlegung mittels radialer Basisfunktionen (Bachelor)
  • Konvergenz und Stabilität adaptiver Multilevelverfahren (Master)

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