CTU FEE Moodle
Numerical Analysis
B232 - Summer 23/24
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. Direct motivation to SRL (Self-Regulated Learning).
Course outlines
1. Overview of the subject of Numerical Analysis. Approximation of functions, polynomial interpolation.
2. Errors of polynomial interpolation and their estimation.
3. Hermite interpolating polynomial. Splines.
4. Least squares approximation.
5. Numerical differentiation. Richardson's extrapolation.
6. Numerical integration (quadrature).
7. Error estimates and stepsize control. Gaussian and Romberg integration.
8. Integration over infinite ranges. Tricks for numerical integration.
9. Root separation. Basic root-finding methods.
10. Iteration method, fixed point theorem.
11. Finitary methods of solution of systems of linear equations.
12. Matrix norms, convergence of sequences of vectors and matrices.
13. Iterative methods of solution of systems of linear equations.
14. Reserve.
2. Errors of polynomial interpolation and their estimation.
3. Hermite interpolating polynomial. Splines.
4. Least squares approximation.
5. Numerical differentiation. Richardson's extrapolation.
6. Numerical integration (quadrature).
7. Error estimates and stepsize control. Gaussian and Romberg integration.
8. Integration over infinite ranges. Tricks for numerical integration.
9. Root separation. Basic root-finding methods.
10. Iteration method, fixed point theorem.
11. Finitary methods of solution of systems of linear equations.
12. Matrix norms, convergence of sequences of vectors and matrices.
13. Iterative methods of solution of systems of linear equations.
14. Reserve.
Exercises outlines
1. Instruction on work in laboratory and Maple.
2. 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. Individual work on assessment tasks.
8. Numerical differentiation and integration, modification of tasks.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Individual work on assessment tasks.
12. Solution of systems of linear equations.
13. Submission of assessment tasks.
14. Individual work on assessment tasks; assessment.
2. 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. Individual work on assessment tasks.
8. Numerical differentiation and integration, modification of tasks.
9. Individual work on assessment tasks.
10. Solution of systems of linear equations.
11. Individual work on assessment tasks.
12. Solution of systems of linear equations.
13. Submission of assessment tasks.
14. 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. Math in Maple (B0B01MVM) is an appropriate/recommended prerequisite.