39 hod., optionally

1. Errors in numerical calculations. Numerical methods for one nonlinear equation in one unknown 2. Basic principles of iterative methods. The Banach fixed-point theorem. 3. Norms of vectors and of matrices, eigenvalues and eigenvectors of matrices. Iterative methods for systems of linear algebraic equations– part I. 4. Iterative methods for linear algebraic equations – part II. Iterative methods for systems of nonlinear equations. 5. Direct methods for systems of linear algebraic equations, LU-decomposition. Systems of linear algebraic equations with special matrice – part I. 6. Systems of linear algebraic equations with special matrices – part II. The methods based on the minimization of a quadratic form. 7. Computing inverse matrices and determinants, the stability and the condition number of a matrix. 8. Eigenvalues of matrices – the power method. Basic principles of interpolation. 9. Polynomial interpolation. 10. Interpolation by means of splines. Orthogonal polynoms. 11. Approximation by the discrete least squares. 12. Numerical differentiation, Richardson´s extrapolation. Numerical integration of functions in one variables – part I. 13. Numerical integration of functions in one variables – part II. Numerical integration of functions in two variables.