Numerical Analysis
Numerical Analysis B4B01NUM
| Credits | 6 |
| Semesters | Winter |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 2P+2C |
Annotation
The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent 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.
Study targets
Practical use of numerical methods, also in non-standard situations, where a modification of the task is needed.
Course outlines
1. Overview of the subject of Numerical Analysis.
2. Sources of errors in numerical computations.
3. Approximation of functions, polynomial interpolation.
4. Errors of polynomial interpolation and their estimation.
5. Hermite interpolating polynomial. Splines.
6. Least squares approximation.
7. Basic root-finding methods.
8. Iteration method, fixed point theorem.
9. Basic theorem of algebra, root separation and finding roots of polynomials,
10. Solution of systems of linear equations.
11. Numerical differentiation.
12. Numerical integration (quadrature); error estimates and stepsize control.
13. Gaussian and Romberg integration.
2. Sources of errors in numerical computations.
3. Approximation of functions, polynomial interpolation.
4. Errors of polynomial interpolation and their estimation.
5. Hermite interpolating polynomial. Splines.
6. Least squares approximation.
7. Basic root-finding methods.
8. Iteration method, fixed point theorem.
9. Basic theorem of algebra, root separation and finding roots of polynomials,
10. Solution of systems of linear equations.
11. Numerical differentiation.
12. Numerical integration (quadrature); error estimates and stepsize control.
13. Gaussian and Romberg integration.
Exercises outlines
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. Individual work on assessment tasks.
6. Least squares approximation.
7. Individual work on assessment tasks.
8. Root-finding methods, root separation.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Numerical differentiation and integration, modification of tasks.
12. Submission of assessment tasks.
13. Individual work on assessment tasks; assessment.
2. Individual work - training in Maple.
3. Polynomial interpolation, estimation of errors.
4. Individual work on assessment tasks.
5. Individual work on assessment tasks.
6. Least squares approximation.
7. Individual work on assessment tasks.
8. Root-finding methods, root separation.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Numerical differentiation and integration, modification of tasks.
12. Submission of assessment tasks.
13. Individual work on assessment tasks; assessment.
Literature
[1] Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T.: Numerical Recipes (The Art of Scientific Computing), Cambridge University Press, Cambridge, 2002, ISBN 0-521-75033-4.
[2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997.
[3] Maple User Manuals and Programming Guides, Maplesoft, a division of Waterloo Maple Inc. (http://www.maplesoft.com/documentation_center/)
[2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997.
[3] Maple User Manuals and Programming Guides, Maplesoft, a division of Waterloo Maple Inc. (http://www.maplesoft.com/documentation_center/)
Requirements
Linear Algebra, Calculus.
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Study Information System (KOS)
