714-0781 – Numerical methods and statistics (NMS)

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.

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.

1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.

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.