Course Unit Code | 310-2220/01 |
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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 * | Second 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 | Course succeeds to compulsory courses of previous semester |
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Name of Lecturer(s) | Personal ID | Name |
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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| KRC76 | Mgr. Jiří Krček |
Summary |
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The course is devoted to basic numerical methods of the linear algebra and mathematical analysis and to basic methods of analysing statistical data. The following themes will be presented: 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, estimations of statistical parameters and
testing of hypotheses. 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 and with the basic methods of analysing statistical data. The main accent lays in explanations of fundamental principles of methods so that the students should know to choose appropriate methods for problems arising in the other courses of the study or in the technical practice. An important ingredient of the course consists in the algorithmic implementation of methods and in the utilization of existing computer programms for numerical computations and statistical analyses.
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.
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Course Contents |
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1st Course contents, the issue of errors, stability of calculations.
2nd Solution of nonlinear equations, separation of roots, the simplest methods.
3rd Newton's method and fixed-point iterations.
4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
5th Eigenvalues and eigenvectors, numerical calculation.
6th Iterative methods for solving linear equations.
7th Interpolation by polynomials and splines.
8th Least squares approximation.
9th Numerical differentiation and integration.
10th Extrapolation in the calculation of integrals. Gaussian integration formulas.
11th One-step methods for solving initial value problems for ordinary differential equations.
12th Multi-step methods.
13th Statistical data processing, empirical characteristics.
14th Parameter estimation and testing of hypotheses. |
Recommended or Required Reading |
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Required Reading: |
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1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. |
1. Kučera, R.: Numerické metody, Skriptum VŠB-TU Ostrava, 2007. (na http://mdg.vsb.cz/M/)
2. Otipka, P., Šmajstrla, V.: Pravděpodobnost a statistika. Skriptum VŠB-TU Ostrava, 2007. (na http://mdg.vsb.cz/M/)
3. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. |
Recommended Reading: |
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1. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003.
2. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper
Saddle River, NJ 07459, 1999.
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1. Kubíček, M., Dubcová, M., Janovská, D.: Numerické metody a algoritmy. 2. vyd., VŠCHT Praha 2005.
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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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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 20 | 5 |
Examination | Examination | 80 (80) | 30 |
Písemná zkouška | Written examination | 60 | 25 |
Ústní zkouška | Oral examination | 20 | 5 |