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Numerical Mathematics

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2130/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Third Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KUC14prof. RNDr. Radek Kučera, Ph.D.
KRC76Mgr. Jiří Krček
SVO19Mgr. Ivona Tomečková, Ph.D.
JAH0037Mgr. Monika Jahodová, Ph.D.
Summary
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
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
1. Introduction (precisions, methods)
2. Interpolation and splines
3. Least square method
4. Roots finding (bisection method, Newton's .method)
5. Linear solver (Lu-factorization)
6. Iteratice methods for linear equations
7. Numerical intergrations
8. ODE solver
Recommended or Required Reading
Required Reading:
Boháč, Z.: Numerical Methods and Statistics. VŠB-TU Ostrava, 2005.
ISBN 80-248-0803-X
Kučera, R.: Numerické metody. VŠB-TU Ostrava 2007, na http://www.studopory.vsb.cz, http://mdg.vsb.cz/portal,ISBN 80-248-1198-7.
Boháč, Z.: Numerical Methods and Statistics. VŠB-TU Ostrava, 2005.
ISBN 80-248-0803-X
Recommended Reading:
Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007, ISBN 978-3-540-34658-6.
Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003, ISBN 0-521-00794-1.
Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper
Saddle River, NJ 07459, 1999, ISBN-13: 9780139491573.
Kubíček, M., Dubcová, M., Janovská, D.: Numerické metody a algoritmy. 2. vyd., VŠCHT Praha 2005, ISBN 80-7080-558-7.
Dalík, J.: Numerické metody. Skriptum VUT, Brno 1997, ISBN 80-214-0646-1.
Vitásek, E.: Numerické metody. SNTL, Praha 1987.
Quarteroni, A., Sacco, R., Saleri F.: Numerical mathematics. 2nd ed. Berlin: Springer, c2007. Texts in applied mathematics, 37. ISBN 978-3-540-34658-6.
Mathews, J. H., Fink, K. D.: Numerical methods using MATLAB. 4th ed. Upper Saddle River: Pearson Prentice Hall, c2004. ISBN 0-13-065248-2.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Graded creditGraded credit100 (100)51
        Praktická částWritten test80 45
        Teoretická částWritten test20 5