The study course is intended to acquaint students with the mathematical apparatus on which the mathematical models used in physics and speciality study course are based. The study work is focused on the development of problem-solving skills, at the same time giving students the opportunity to understand the logical structure of mathematics and its ability to structure various practical tasks. Topics covered: introduction to analysis, limits, continuity; derivative and differential, their applications; matrices and determinants; systems of linear equations; analytical geometry: vectors, lines, surfaces; indefinite and definite integrals, their applications; ordinary differential equations; differential calculus of functions of several variables; improper, double and triple integrals; series of numbers and functions.