Mathematics - Bc.

Systems of n ordinary linear differential equations of the first order for n
functions: definition, representation at matrix form, methods of solution of
systems of 2 equations for 2 functions, Euler method for homogeneous systems of
n equations for n functions. Integral calculus of functions of several
independent variables: two-dimensional integrals, three-dimensional integrals,
vector analysis, line integral of the first and the second kind, surface
integral of the first and second kind. Infinite series: number series, series
of functions, power series.
Basic principles of the numerical mathematics, errors of numerical methods.
Solving of simple equations: bisection method, regula-falsi, Newton method,
basic iterations. Systems of linear equations: Gauss algorithm, LU-
factorisation, Jacobi and Gauss-Seidel iterative method. Interpolation and
approximation: interpolating polynomials, cubic interpolating splines, method
of least-squares. Numerical differentiation, quadrature rules: Newton-Cotes
formulas, composed formulas, extrapolation and Romberg method, Gauss quadrature
formulas.Initial problems for the ordinary differential equations: Euler, Runge-
Kutta and multistep methods, solution of system of equations.