| Course Unit Code | 714-0386/03 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Third Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 714-0366 | Mathematics I |
| 714-0367 | Mathematics II |
| Name of Lecturer(s) | Personal ID | Name |
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| MOR74 | Mgr. Zuzana Morávková, Ph.D. |
| Summary |
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| The course is devoted to basic numerical methods of the linear algebra and mathematical analysis: iterative methods for solving of nonlinear equations, direct and iterative methods for solving of linear systems, eigenvalue problems, interpolation and approximation of functions, numerical computation of derivatives and integrals, solving of ordinary differential equations. The programming system Matlab is used during the course. |
| Learning Outcomes of the Course Unit |
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The aim of this course is to acquaint students with the numerical solution of mathematical problems that arise in the other courses of their study and in the technical practice. The main accent lays in explanations of fundamental principles of numerical methods with emphases their general properties. It should lead to the ability in concrete situations to decide whether a numerical procedure is a suitable tool for solving a particular problem. An important ingredient of the course consists in the algorithmic implementation of methods and in the utilization of existing computer programs specialized for numerical computations.
The graduate of this course should know:
• to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method;
• to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies;
• to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization. |
| Course Contents |
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1. Introduction (precisions, methods)
2. Roots finding (bisection method, Newton's .method)
3. Linear solver (Lu-factorization)
4. Iteratice methods for linear equations
5. Interpolation and splines
6. Least square method
7. Numerical intergrations
8. ODE solver |
| Recommended or Required Reading |
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| Required Reading: |
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1. Boháč, Z.: Numerical Methods and Statistics. VŠB-TU Ostrava, 2005.
ISBN 80-248-0803-X |
| 1. Kučera, R.: Numerické metody. VŠB-TU Ostrava 2007, na http://www.studopory.vsb.cz, http://mdg.vsb.cz/portal,ISBN 80-248-1198-7. |
| Recommended Reading: |
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1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN 978-3-540-34658-6.
2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003, ISBN 0-521-00794-1.
3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper
Saddle River, NJ 07459, 1999, ISBN-13: 9780139491573. |
1. Kubíček, M., Dubcová, M., Janovská, D.: Numerické metody a algoritmy. 2. vyd., VŠCHT Praha 2005, ISBN 80-7080-558-7.
2. Dalík, J.: Numerické metody. Skriptum VUT, Brno 1997, ISBN 80-214-0646-1.
3. Vitásek, E.: Numerické metody. SNTL, Praha 1987.
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Graded exercises evaluation | Graded credit | 100 | 51 |