TUDMATH SS2024 Modul Math-Ba-MOSIM: Modellierung und Simulation

Course Description

Mathematical modelling and numerical simulations form one of the cornerstones of applied mathematics in that they establish a link between mathematics and other life sciences. In this lecture we discuss more advanced aspects of mathematical modelling. We begin our journey with systems of interacting particles as a modelling tool. We shall cover the macroscopic equations their dynamics gives rise to. These equations (partial differential equations) belong to a certain class of PDEs that are wide-spread in many contexts and applications in the life sciences. Using the method of finite differences we will discuss their numerical implementation, simulation, and the visualisation of the associated solutions. Based on the theoretical and numerical aspects, we shall discuss systems that exhibit very dynamics: the formation of interesting pattern such as, for instance, on animal coating, based on the so-called Turing Mechanism, named after Alan Turing in 1952.

Requirements

knowledge of the content of the following modules is expected Math-Ba-AN10, Math-Ba-AN20, Math-Ba-AN40, Math-Ba-LA10, Math-Ba-LA20, Math-Ba-NM10, Math-Ba-NM20, Math-Ba-PR10, Math-Ba-PR20