- Numerical sequences and their boundaries: definitions, examples, properties.
- Numerical Functions: Concept of Continuous Function, Examples of Continuous and Burst Functions.
- Derivative of a numerical function: definitions, examples, properties.
- Initial (indefinite integral) of a numerical function: definitions, examples, properties. The Riemann integral is defined: examples, properties.
- Numerical series, the concept of convergent numerical series, examples. The notion of a power series. A number of Taylor numerical functions, examples.
- Systems of linear equations: examples, methods of solution.
- The concept of the matrix, the multiplication of matrices. Definition of a matrix, calculating determinant, examples.
- The concept of linear space, dimensionality of space, linear independence of the system of vectors, the linear framework of the system of vectors, basis.
- Concept of differential equation, solution of differential equation. Solving differential equations of the first order with separable variables.
- Linear differential equation of the nth order with constant coefficients: a general solution of a homogeneous equation.
- Direct and planes in space: the equation of a straight line on a plane passing through two given points, an equation of a plane in space passing through three given points. Ways of direct problem in space.
- The mutual arrangement of the straight line and the plane in space. Finding the distance from a given point to a given plane in space.

*Note.* During the response, the applicant must demonstrate general awareness of the above concepts, be able to explain their application to the solution of specific tasks, be able to give examples. Knowledge of the wording of the corresponding theorems in full, as well as knowledge of their proofs is optional.

**List of recommended literature**

- Kudryavtsev LD Short course of mathematical analysis. – M .: Nauka, 1989.
- Gelfand I. M., Lectures on linear algebra. – M.: Science, 1970.
- Pontryagin L.S. Ordinary differential equations. – Moscow: Nauka, 1974.
- Borisenko O.A., Ushakova L.M. An analytical geometry. – X.: Basis, 1993.

Approved at the meeting of the Academic Council of the Faculty of Mathematics and Informatics, Minutes No. 1 dated 01.02.2017

Dean of the Faculty of Mathematics and Informatics G. M. Zholtkevich

Approved at the meeting of the admissions committee, protocol No. 2 dated 10.04.2017

O. Anoshenko, Executive Secretary of the Admissions Committee