Numerical Analysis
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| B4B01NUM | Z,ZK | 6 | 2P+2C | Czech |
- Garant předmětu:
- Mirko Navara
- Lecturer:
- Mirko Navara
- Tutor:
- Mirko Navara, Aleš Němeček
- Supervisor:
- Department of Mathematics
- Synopsis:
-
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.
- Requirements:
-
Linear Algebra, Calculus.
- Syllabus of lectures:
-
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.
- 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. 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.
- Study Objective:
-
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).
- 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, 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/)
- Note:
- Further information:
- https://moodle.fel.cvut.cz/courses/B4B01NUM
- Time-table for winter semester 2023/2024:
-
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon Tue Wed Thu Fri - Time-table for summer semester 2023/2024:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Open Informatics - Computer Science 2016 (compulsory course of the specialization)
- Open Informatics (compulsory course of the specialization)
- Medical electronics and bioinformatics (compulsory elective course)
- Open Informatics - Artificial Intelligence and Computer Science 2018 (compulsory course of the branch)