Ruprecht-Karls-Universität Heidelberg
Siegel der Universität Heidelberg

Modelling and Applied Analysis

Objectives

Systems in Materials Science, Biology, Medicine and other fields often display a complex behaviour. Typically these systems have a nonlinear structure. Furthermore, physical mechanisms in vastly different length and time scales play a role in determining the effective behaviour of the system. In order to efficiently  compute and predict the observable dynamics, it is important to derive mesoscopic models which capture the effective behaviour of the system. Analytical methods on the one hand provide tools in the derivation of such models.  These effective models then can be investigated by a combination of analytical and numerical tools.

The objective of the specialization "Modelling and Applied Analysis" in the International Masters Program of Scientific Computing is to study analytical methods and tools which are useful in the derivation, analysis, simulation and optimization of complex systems.  Our aim ist to understand the spatial and temporal behaviour of these systems in dependence of their intrinsic parameters and initial data. In particular, the focus of this program lies in the investigation of problems arising in the field of Materials Science, Biology and Medicine.

Researchers in this field

  Prof. Anna Marciniak-Czochra

  Prof. Hans Knüpfer


Course Offerings / Tentative Study Plan:

Foundation courses

  • Functional Analysis
  • Introduction to PDE
  • Introduction to Numerics/Numerics

These courses are offered as part of the Mathematics Curriculum.

Other courses relevant to this specialication

Mathematics:

  • Nonlinear PDE
  • Nonlinear Functional Analysis
  • Dynamical Systems
  • Calculus of Variations
  • Homogenization Theory

Computer Science:

Seminars & Practicals

  • Seminar covering recent topics of PDEs
  • Seminar covering Numerics and its application to PDE
  • Seminar covering Modelling

Application Fields

  • Materials Science
  • Developmental Biology
  • Systems Biology
  • Medicine
  • Fluid Dynamics

Sample Plan of Study

Winter Term 1

  • Dynamical Systems
  • Nonlinear Partial Differential Equations
  • Numerics of Partial differential equations
  • Seminar (Modelling in PDEs)

Summer Term 1

Winter Term 2


Summer Term 2

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