Cykl wykładów w ramach projektu ''Zamawianie kształcenia na kierunkach technicznych, matematycznych i przyrodniczych - pilotaż''

Prof. Mads Sorensen  - Department of Mathematics,
Technical University of Denmark (Lyngby)

Mathematical Modeling of Industrial Problems
(opis wykładów niżej)

poniedziałek 9 maja, 16-18 s. 4070

wtorek 10 maja, 16-19 s. 4050

środa 11 maja, 16-18 s. 4070

czwartek 12 maja, 16-19 s. 4070

Content:

Lecture 1 (2 hours):
Short introduction to drug development.
Cartoon models of the blood coagulation cascade.
One simple model of the blood coagulation cascade.
Perfusion experiment.
Introduction to enzyme kinetics.

Lecture 2 (2 hours):
Enzyme kinetics. The equilibrium approximation.
The quasi steady state approximation.
Enzyme inhibition. Competitive inhibition.
Allosteric inhibitors.
Cartoon model for the perfusion experiment.

Lecture 3 (2 hours)
Set up of one to two dynamical equations for the perfusion experiment.
Lumped model.
Enzyme kinetics. Cooperativity.
Enzyme kinetics and singular perturbation theory.
Mention numerical methods for ODEs.

Lecture 4 (2 hours)
Influence of blood flow and diffusion.
Set up reaction-diffusion-advection models.
Dynamical boundary conditions.
The finite element method.

Lecture 5 (2 hours)
The finite element method.
Presentation of results.
Other cases. (Examples: Float Zone manufacturing of single crystal silicon
wafers. Ultra sound inspection of welds).