Code: 17AMPMSB Mathemetical Software for Biomedicine
Lecturer:  Weekly load: 1+1 Assessment: KZ
Department: 17101 Credits: 2 Semester: S
Description:
Some physical models application in biomedical processes and their numerical solution with the aid of mathematical SW, partial differential equations and formulation of respective problems, classification of linear 2nd order PDEs, examples of individual types of equations and formulation of problems, numerical solution of the problems by means of the finite difference method.
Contents:
1. Mathematical SW as an aid for solving problems - general principles
2. Elementary physical processes and their modeling.
3. Selected models for respiratory system.
4. Selected blood flow processes and their modeling.
5. Population dynamics.
6. Linear 2nd order partial differential equations classification.
7. Formulation of problems for Poisson (Laplace) equation.
8. Finite difference method for solving Dirichlet boundary value problem for Poisson (Laplace) equation in 2D, 3D.
9. Formulation of problems for a heat transfer equationin 1D, 2D.
10. Finite difference method for solving initial and boundary value problem for a heat transfer equation in 1D, 2D.
12. Formulation of problems for a wave equation.
13. Finite difference method for solving initial and boundary value problem for a wave transfer equation in 1D, 2D.
14. Numerical solution of an inverse problem for PDEs.
Recommended literature:
Studijní materiály
Doňar B., Zaplatílek K., -- MATLAB pro začátečníky, 1. díl, BEN, 2003
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
E. Feuerstein - Řešené příklady z numerické matematiky, pracovní texty

Doporučená literatura:
Doňar B., Zaplatílek K., MATLAB tvorba uživatelských aplikací, 2.díl, BEN, 2006
Moler C.: Numerical computing with MATLAB, Mathworks, PDF
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:
Mathematical models in biomedicine, partial differential equations, wave equation, heat transfer equation, Laplace equation, Poisson equation, diffusion equation