Theory and Applications of Ordinary Differential Equations (CBL component)

URL study guide

https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2MBC20&collegejaar=2025&taal=en

Omschrijving

Ordinary differential equations occur as models of processes in which the state of a system determines its change. Therefore they describe population dynamics, chemical reactions, vibrations, electrical circuits etc.

In this course we will introduce several methods from the analysis of differential equations  that help us to understand such systems, and we will apply this in a  modelling project that focusses on a concrete problem.

Initial value problems for ordinary differential equations. Elementary solution techniques for different types of equations. Existence and uniqueness of solutions. Maximal solutions, global existence and blowup. (Systems of) linear ordinary differential equations with constant coefficients. Phase space analysis. Types of equilibria. Stability of non-linear autonomous systems. Vector fields, flows and diffeomorphisms. Principle of linearized stability.  Modelling assignment.

Doelstellingen

Students are able to

Recognize and solve elementary types of scalar ODEs, and linear (systems of) ODEs with constant coefficients

Understand and apply the basic existence and uniqueness results on initial value problems for ODEs, determine qualitative properties and behavior of ODEs with respect to global existence or blowup of solutions, their dependence on initial values and parameters

 Apply geometric concepts (flows, vector fields, diffeomorphisms) in the interpretation of autonomous ODEs and their solution properties and techniques, and connect these concepts to the applications
 
 Recognize first integrals and Lyapunov functions for ODEs, and use these to derive qualitative results
 
 Find stationary points of autonomous ODEs, and analyze their stability.
 
 Design a simple ODE model of a real world problem, reflect on its  assumptions and validity, apply the general theory to it, interpret the results, and critically assess the interplay between modelling, theory, and numerics in this design

Beoordelingsmethode

Written examination