Some physical models application in biomedical processes and their numerical solution with the aid of mathematical SW is presented and practical applications are solved.
Contents:
1. Systems of linear algebraic equations and their solution.
2. Solving nonlinear algebraic systems of equations.
3. Processes described by systems of algebraic equations.
4. Interpolation, approximation of sets of data and applications.
5. Ordinary differential equations and problems formulation.
6. Numerical solution of the problems described by ODEs.
7. Examples of population models, pharmacokinetics models.
8. Nonlinear models and methods of their solution.
9. Linear 2nd order partial differential equations classification.
10. Formulation of problems for PDEs and methods of solution.
11. Diffusion processes in 2D, (stationary as well as non-stationary).
12. Modeling of bacterial population growth.
13. Formulation of problems for a wave equation.
14. Selected biomedical fluid flow problems.
Recommended literature:
Holčík J., -- Modelování a simulace biologických systémů, skriptum ČVUT-- FBMI, 2006
Kvasnica J.,-- Matematický aparát fyziky, Academia, 2. vyd. 1997
Dont M. - Úvod do parciálních diferenciálních rovnic
Doporučená studijní literatura:
Hannon B., Ruth M. - Modeling Dynamic Biological Systems, Springer, 1999
Hoppensteadt F., Peskin Ch. - Modeling and Simulation in Medicine and the Life Sciences, Springer, 2002
Keywords:
Linear algebraic equations, nonlinear algebraic equations, ordinary differential equations, partial differential equations, wave equation, modeling of biomedical systems and their solution, examples of application in biomedicine.