Numerical vector spaces. Matrices, elementary matrix transformations and the rank of a matrix. Coordinates of vectors with respect to a given basis, the concept of a determinant, systems of linear equations. Iteration methods for their solution (Jacobi and Gauss-Seidel). Scalar and vector products, orthogonal and orthonormal bases. The concepts of a vector and a combined product, applications. Elements of the nalytical geometry, planar and spatial linear and quadratic objects. Real functions, domains and ranges. Elementary functions. The concept of an inverse function, inverses to exponential and trigonometric functions. Elements of the theory of polynomials, fundamental theorem of algebra. The concept of a limit, some rules and methods for its computation. The concept of a derivative, geometrical and physical meaning, rules for its computation.Derivatives of inverse functions, L´Hospital rule, Taylor formula. The concept of a primitive function and an indefinite integral, some elementary methods of integration. Riemann integral, numerical integration improper integral, geometrical and physical apllications. Differential calculus of functions of n variables, domains, partial and directional derivatives. Total differential, local extremes. The concept of an ordinary differential equation (ODE), 1-st order ODE, homogenous higher-order linear ODE with constant coefficients. The numerical method of nets.