Course plan. Mathematical modeling MMG510
spring 2009.

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 MVF31 we will have lectures and exercises during first two weeks and later we will have discussions on the projects at this time.

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%).

week 12(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 13 (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. Exercises on stability. 

         Thirsday 10:00 : First integrals. 

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

week 14 (III) ()

         Monday    Master equation for chemical kinetics by Monte Carlo method. The Gillespie method.Home assignment N1

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

Holidays

week 17 (IV) ()

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

Wednesday - other activities 

week 18 (V) ()

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

Wednesday    13.00 Exercises, projects

         Thirsday   10:00:Lyapunovs method. exercises on stability. Hopf bifurcation.

week 19 (VI) ()

         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.

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

week 22 (IX) ()

         Wednesday   Examination.

         Extra day:  Consultation before examination.