Basic problems of the numerical mathematics, errors in computations. Solving of
equation f(x)=0: bisection method, regula-falsi, iterative method, Newton´s
iteration, roots of polynomials. Numerical solution of systems of linear
algebraic equations: LU-factorization, iterative methods, condition number of
matrix, ill-conditioned matrices. Numerical solution of systems of nonlinear
equations: Fixed-point iteration, Newton’s method. Interpolation and
approximation of functions: Polynomial interpolation, interpolation by cubic
spline functions, least squares approximation. Numerical integration: Trapezoid
rule, Simpson’s rule, Richardson extrapolation, Monte Carlo method.
Characteristics of population and sample, measures of central tendency,
measures of dispersion and skewness, sampling distributions, point estimate,
confidence interval, moment method, maximum likelihood method, testing
hypotheses.