Numerical Methods

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. Introduction, numerical methods, principles.

2. Errors, rounding errors, errors of a method.

3. Iterative methods for finding roots of equation f(x)=0.

4. Solving systems of linear algebraic equations - direct methods.

5. Solving systems of linear algebraic equations - iterative methods.

6. Solving systems of non-linear algebraic equations - Newton method.

7. Numerical differentiation.

8. Numerical integration.

9. Principles of numerical methods for solving problems for ODEs.

One step methods for solving initial value problem for 1st order ODE.

10. One step methods for solving initial value problem for a system of 1st order ODEs.

12. One step methods for solving initial value problem for nth order ODE.

13. Principles of multi step metods.

14. Praktical application of differential equations in biomedical engineering.

Syllabus of tutorials:

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

2. Errors, round off error ad error of a method. Iterative methods - examples.

3. Iterative methods for finding roots of equation f(x)=0.

4. Solving systems of linear algebraic equations - direct methods.

5. Solving systems of linear algebraic equations - iterative methods.

6. Solving systems of non-linear algebraic equations - Newton method.

7. Numerical differentiation.

8. Numerical integration.

9. Principles of numerical methods for solving problems for ODEs.

One step methods for solving initial value problem for 1st order ODE.

10. One step methods for solving initial value problem for a system of 1st order ODEs.

12. One step methods for solving initial value problem for nth order ODE.

13. Principles of multi step metods.

14. Praktical application of differential equations in biomedical engineering.

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:

Základní studijní literatura:

Vitásek E.: Numerické metody, SNTL, Praha 1987

Doporučená studijní literatura:

Černá R., Machalický M., Vogel J., Zlatník Č.: Základy numerické matematiky a programování, SNTL, Praha 1987

Benda J., Černá R.: Numerická matematika, doplňkové skriptum, Vydavatelství ČVUT, 1994

Moler C.: Numerical computing with MATLAB, Mahworks, PDF

Feuerstein, E.: - řešené příklady k přednáškám - preprint

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 Biomedicínský inženýr - prezenční (compulsory course)