Numerical Analysis

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Cybernetics

Synopsis:

The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent and (ordinary and partial) differential equations and systems of linear equations. Emphasis is put on estimation of errors, practical skills with the methods and demonstration of their properties using Maple and computer graphics.

Requirements:

The first two courses of bachelor studies, mathematics and programming.

Syllabus of lectures:

1. Overview of the subject of Numerical Analysis

2. Approximation of functions, polynomial interpolation

3. Errors of polynomial interpolation and their estimation

4. Hermite interpolating polynomial. Splines

5. Least squares approximation

6. Basic root-finding methods

7. Iteration method, fixed point theorem

8. Basic theorem of algebra, root separation and finding roots of polynomials

9. Solution of systems of linear equations

10. Numerical differentiation

11. Numerical integration (quadrature); error estimates and stepsize control

12. Gaussian and Romberg integration

13. One-step methods of solution of ODE's

14. Multistep methods of solution of ODE's

Syllabus of tutorials:

1. Instruction on work in laboratory and Maple

2. Individual work - training in Maple

3. Polynomial interpolation, estimation of errors

4. Individual work on assessment tasks

5. Least squares approximation

6. Individual work on assessment tasks

7. Root-finding methods, root separation

8. Individual work on assessment tasks

9. Solution of systems of linear equations

10. Numerical differentiation

11. Numerical differentiation and integration, modification of tasks

12. Individual work on assessment tasks

13. Solution of ODE's

14. Individual work on assessment tasks; assessment

Study Objective:

Basic methods of approximation, numerical differentiation and integration, numerical solution to algebraic, transcendent and differential equations.

Study materials:

[1] Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T.: Numerical Recipes (The Art of Scientific Computing), Cambridge University Press, Cambridge, 1990.

[2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)