714-0886 – Numerical Methods (NumMeth)

The course is an introduction to the numerical methods. The main goal consists in explanations of fundamental numerical principles so that students should be able to decide about an appropriate method for problems arising in the other courses or in the technical practice. An important ingredient is the algorithmic implementation of numerical methods and the usage of the standard numerical software. 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. It is necessary to complete Mathematics 1 and Mathematics 2 courses or their equivalents.

The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis. The following topics are presented: direct and iterative methods for solving systems of linear equations; eigenvalue problems; iterative solving of nonlinear equations; interpolation and approximation of the function data; numerical computation of integrals and derivatives; numerical solving of initial value problems for ordinary differential equations; using MATLAB in numerical computations.

1. Burden, R. L., Faires, J. D.: Numerical Analysis. Cengage Learning, 2011 2. Chapra, S., Canale, R.: Numerical Methods for Engineers. McGraw-Hill Education, 2009.

1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. 2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. 3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999.