Fundamentals of applied mathematics

Lecturer:

Tutor:

Supervisor:

Department of Natural Sciences

Synopsis:

Some physical models application in biomedical processes and their numerical solution with the aid of mathematical SW is presented and practical applications are solved.

Requirements:

Assessment:

Maximum 3 absences during the semester for serious reasons like sickness, injury etc. (medical certificate required).

Minimum 50% (i.e. 10 pts) evaluation at each of the 2 tests, each test consisting of 4 tasks, a task evaluated max. 5 pts each (the tests are taken in 6th and 13th week of the semester).

Exam:

1. Assessment recorded in „KOS? and signed by respective teacher in student?s “Index?,

2. Minimum 50% evaluation at the exam test. Exam test comprises of 10 tasks, a single task evaluated max 10% each.

Evaluation scale: less than 50% - F, 50-59% - E, 60-69% - D, 70-79% - C, 80-89% - B, 90-100% - A.

Syllabus of lectures:

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.

Syllabus of tutorials:

1. Practical examples of systems of linear algebraic equations and their solution.

2. Solving nonlinear algebraic systems of equations.

3. Examples of processes described by systems of algebraic equations.

4. Biomedical data interpolation,

approximation of sets of biomedical data by means of the least squares method.

5. Solving initial value problems for ordinary differential equation.

6. Numerical solution of the problems described by ODEs.

7. Solving examples of population models, pharmacokinetics models.

8. Examples of nonlinear models and methods of their solution.

9. Linear 2nd order partial differential equations classification.

10. Solving selected problems for PDEs, testing methods of solution.

11. Diffusion processes in 2D, (stationary as well as non-stationary) examples.

12. Modeling of bacterial population growth examples.

13. Formulation of problems for a wave equation and examples.

14. Selected biomedical fluid flow problems.

Study Objective:

The goal of the subject is to introduce to the students models and some methods of solving selected biomedical problems with the aid of mathematical SW.

Study materials:

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Navazující magisterský studijní obor Přístroje a metody pro biomedicínu (compulsory course)