714-0386 – Numerical Mathematics (NM)

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.

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.

1. Boháč, Z.: Numerical Methods and Statistics. VŠB-TU Ostrava, 2005. ISBN 80-248-0803-X

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.