Course plan. Mathematical modeling MMG510
spring 2008.

Teaching will include lectures, exercises, 3 assignments to be done at home, and a larger project done in working groups.

We will study during 7 weeks and have lectures and exercises on Mondays at 10.00 in MVF21 and on Thirsdays in  MVF21 at 10.00.

On Wednesdays at 13:00 in MVF21 we will have lectures and exercises during first two weeks and later partially exercises and parially discussions on the projects.

One meeting per week with each working group for discussing the projects must  take place at the Mathematical Center.

The week eight (VIII) will be for presentation of projects 30 minutes for every group. A working group can consist of maximum 3 people.

A short 2 hours written examination over the theoretical part of the course will take place at the end.

Well done home assignments will be counted as a bonus for the corresponding part of the written examination.

Total points for the course will be an average of points for the project (60%) and for the examination (40%).

Some changes in the order of chapters can be done.
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week 14(I) ()

Monday 10.00:  Introduction. En example of a problem with modeling by ordinary differential equations, PDE and stochastic processes.

Wednesday    13.00: Introduction. En example of a problem with modeling by ordinary differential equations, PDE and stochastic processes.

Thirsday   10:00: Three views on diffusion: stochastic, kinetic, PDE. Modeling of different types of transport processes by PDE and kinetic models.

week 15 (II) ()

Monday    10.00: Ordinary differential equations. Phase portrait. Linear systems of ordinary differential equations.

Wednesday    13.00: Stability of stationary points and solutions of differential equations. Ljapunov functions. Exercises on stability.

Thirsday 10:00 : First integrals. Periodic solutions to ODE. Poincaré-Bendixson theorem. Home assignment N1

OBS!!!  Important to have a plan for the project.

week 16 (III) ()

Monday    10:00: First integrals. Periodic solutions to ODE. Poincaré-Bendixson theorem. Examples of periodic solutions.

Wednesday    13.00 Exercises, projects

Thirsday   10:00:Hopf bifurcation. Parameter dependence of models. Bifurcations. Bifurcation diagrams.

week 17 (IV) ()

Monday    Dimensions analysis and scaling. Equations in dimensionless variables. Asymptotic methods. Secular terms. Method with two time scales.

Wednesday    13.00:Exercises, projects

Thirsday  10:00: Asymptotic methods. Averaging method.Home assignment N2

week 18 (V) ()

Monday    Master equation for chemical kinetics by Monte Carlo method. The Gillespie method.Home assignment N3

week 19 (VI) ()

Monday - Monte Carlo methods for a stochastic model for particles. General and direct modeling.

Wednesday - other activities

Thirsday   10:00: Monte Carlo methods for a stochastic model for particles. General and direct modeling.

week 20 (VII) (14 – 16 May)

Monday    10:00: Non-linear waves in reaction - diffusion processes.

Wednesday    13.00:  Exercises, projects

Thirsday   Non-linear waves in reaction - diffusion processes.

week 21 (VIII) ()

Monday    10:00: Projects presentations .

Wednesday    13.00:  Exercises, projects

Thirsday   10:00: Projects presentations .

week 22 (IX) ()

Wednesday   Examination.

Extra day:  Consultation before examination.

Alexei Heintz <heintz@math.chalmers.se>