Course plan. Mathematical modeling MMG510, MVE160

Teaching will include lectures, exercises, 2 assignments to be done at home and giving two bonus points each, and a large project done in working groups.

We will study during 8,5 weeks and have lectures and exercises on Mondays at 10.00 in MVF31 and on Thirsdays in  MVF31 at 8.00.

On Tuesedays at 15:00 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.

A part of  the weeks eight and nine will be devoted to the presentation of projects 30 minutes for every group. A working group can consist of maximum 3 people.

A 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%).
The textbook for the course is: Arrowsmith D.K. , Place C.M.: Ordinary Differential Equations.
 A Qualitative Approach with Applications. Chapmann and Hall. (1982).The reference to the book below is A.P.
The order of chapters can be slightly shifted.

week 12(I) ()

        Monday 15:15  Introduction to ODE. Phase portrate, trajectories. Particular examples. A.P. Intorduction. Exercises chapter 1: 3; 4c),f); 5; 19a),d); 25; 27iv); 29a)
     Tuesday    15.15:  Topics for projects.
                                 En example of a problem with modeling by ordinary differential equations, PDE and stochastic processes. Lecture notes 
                                 Modeling of different types of transport processes by PDE, kinetic models and stochastic processes.
      Thirsday   8:00:   Linear systems of ordinary differential equations. Classification of matrices. A.P. Chapter 2.1-4. Exercises chapter 2: 4; 6; 9b),c),d); 13b),c),e).

week 13 (II) ()

         Monday    15.15: Linear systems of ordinary differential equations. The evolution operator. Affine systems.  A.P.Chapter 2.5,6,7. Exerciseschapter 2. 21 a),e); 3b);34c)
      Tuesday    15.15:  Exersises on linear systems of ordinary differential equations. A.P.Chapter 2
       Thirsday     8:00 : Stability of stationary points and solutions of non-linear differential equations. Exercises on stability. A.P.Chapter 3.1,2,3,5
      Home assignment N1    

OBS!!!  Important to have a plan for the project at the end of the second week.

week 14 (III) ()

         Monday  15:15:   Master equation for chemical reactions. The Gillespie method. Lecture notes and a paper by Gillespie
       Tuesday  15.15:  Exercises, projects

week 15 (IV) ()

       Monday    15.15: Lattice Boltzmann equation for modeling flows and diffusion. Lecture notes
     Tuesday     15.15:  Exercises, projects

Holidays and examination weeks
week 18 (V) ()

         Monday    15:15:  Poincaré-Bendixsons theorem. Examples of periodic solutions A.P.Chapter 3.8,9
      Tuesday    15:00 Exercises, projects
         Thirsday   8:00: Van Der Pol oscillator.  Lienard equation.  A.P. 4.4, 5.1

week 19 (VI) ()

         Monday   15:15: Lyapunovs functions. Lyapunovs method. A.P.  5.4
      Tuesday    15:15:  Exercises, projects
       Thirsday    8:00:. Exercises on Lyapunovs method. A.P.  5.4

week 20 (VII) (14 – 16 May)

         Monday    15:15: Bifurcations. Hopf bifurcation. A.P. 5.5
      Tuesday     15:15:  Exercises, projects
      Thirsday     8:00:   Dimensional analysis. Equations in non-dimensional form. Lecture notes.

week 21 (VIII) ()

         Monday    15:15: Projects presentations .
      Tuesday     15:15:  Projects presentations .
      Thirsday     8:00:    Projects presentations .

week 22 (IX) ()

       Wednesday 1 june ;  8.30 -13.30  Examination