Subject description - B4B01NUM
Summary of Study |
Summary of Branches |
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List of Roles |
Explanatory Notes
Instructions
| B4B01NUM | Numerical Analysis | ||
|---|---|---|---|
| Roles: | PO, PZ, PV | Extent of teaching: | 2P+2C |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Navara M. | Completion: | Z,ZK |
| Lecturers: | Navara M. | Credits: | 6 |
| Tutors: | Navara M., Němeček A. | Semester: | Z |
Web page:
https://moodle.fel.cvut.cz/courses/B4B01NUMAnotation:
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. |
Exercises outline:
| 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. |
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/) |
Requirements:
Linear Algebra, Calculus. Math in Maple (B0B01MVM) is an appropriate/recommended prerequisite.Note:
| Form: classical lectures, work on computer in the laboratory (Maple). |
Keywords:
Interpolation, approximation of functions, numerical differentiation, numerical integration, solution of equations, solution of systems of linear equations. Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| BPOI1_2016 | Computer and Information Science | PO | 3 |
| BPOI_BO_2016 | Common courses | PO | 3 |
| BPBIO_2018 | Common courses | PV | 4 |
| BPOI1_2018 | Artificial Intelligence and Computer Science | PZ | 3 |
| Page updated 30.12.2024 15:51:10, semester: Z/2025-6, Z,L/2024-5, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |