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Special Topics in Software Engineering:

Mathematical Modelling and Simulation of Biological Systems

339.311 1KV Kmet Block

The aim of the course is to introduce students to application of ordinary differential equations, partial differential equations, partial functional differential equations and optimal control theory to model problems arising in biology and simulation of these mathematical models.

Students should be able to derive mathematical model of biological system and its simulation using Mathlab & Simulink.

Lecturer

Prof. Dr. Tibor Kmet, Constantine the Philosopher University, Slovakia
tkmet@ukf.sk

Dates

Date Time Room
Tu 12.6.2007 15:30 - 17:00 BA 9909
We 13.6.2007 15:30 - 17:00 UC 5
Th 14.6.2007 15:30 - 17:00 BA 9907
Fr 15.6.2007 15:30 - 17:00 BA 9907

Contents

Topics will be chosen from the following list

  • ordinary differential equations,
  • partial differential equations,
  • partial functional differential equations and optimal controltheory,
  • steady state and fixed points,
  • stability,
  • numerical solution,
  • creating a mathematical
  • model,
  • modelling and simulating dynamical systems,
  • running simulation.

Exam

Students have to do a project (i.e. to develop a mathematical model of realistic biological system, stability analysis, application of optimal control problem and simulation of the mathematical model using Mathlab & Simulink)

Downloads

Software: Mathlab & Simulink

Literature:

  1. D. J. Higham, N. J. Higham: Matlab Guide, SIAM, 2000.
  2. Mathlab & Simulink Guide, The MathWorks, Inc. 2004
  3. F. Brauer, C. Castillo-Cháves : Mathematical Models in population Biology and Epidemology, Springer, 2000.
  4. P. Fishwick: Dynamic Modeling, SCS, 2002
  5. J. Wu: Theory and applications of partial functional differential equations, Springer, Applied Math. Sciences, 1996