Fundamentals of numerical analysis: random variables; probability and statistics; functions, matrix algebra; eigenvalues and eigenvectors; calculation errors; calculation of function value; approximate solutions of algebraic and transcendent equations. Interpolation of function and approximation of derivative and integral of functions. System of linear algebraic equations: theorems, transformations of equivalence; permutation matrices; solving solutions (Gauss's elimination process, triangular decomposition) and optimal equation ordering (Quasi-optimal methods and Tunney optimal schemes). Space matrices techniques: static and dynamic storage schemes. Matrix inversion: classical methods and matrix inversion lemmas. System of nonlinear algebraic equations: approximate solution; iterative solution corrections; bracketing a root and combined methods; basic and modified Newton-Raphson methods; basic and accelerated Gauss-Seidel methods. Numerical stability and stability of (non)linear systems. Solving of ordinary differential equations (one-stage and multi-stage methods: Runge-Kutta, Euler, predictor corrector). Regression analysis: data model; correlation; residual; WLS; linear regression; sensitivity analysis and model quality assessment. Application in power systems – power flow, short circuit, data modelling, optimization, etc.