• understanding of the main provisions of the theory of differential calculus of functions of several variables and application of knowledge derived for the study of plane and space curves;
• ability to demonstrate knowledge and skills in the theory of integral calculus of functions of several variables and their applications to approximate calculations of values;
• knowledge of the basic theory of differential equations of first and higher orders, the theory of linear homogeneous and nonhomogeneous differential equations, basic theory of systems of linear differential equations of first order and possession of methods of their solution.

prerequsite:
• Higher mathematics, part 1, 2.
• Mathematical processing of geodetic measurements.

Functions of several variables and their research and applications (functions of several variables, methods of job. Geometrical sense. Limit, continuity. Points and break lines. Partial derivatives and total differential of a function of many variables. The directional derivative. The gradient of the function. The extremum of function of several variables. Necessary and sufficient conditions of extremum. The largest and smallest values of the function in the closed area). The geometry of the earth ellipsoid (Spherical trigonometry. The geometry of the earth ellipsoid). Multiple integrals (Double integral. A repeated integral. Calculation of areas and volumes using double integrals. The change of variables in double integral. Calculation of surface area using double integral. Triple integral. Differential characteristics of spherical coordinates. The transition to a triple integral in cylindrical and spherical coordinates). Curvilinear integrals (curve integrals of 1-St and 2-nd type. Green's Formula). Differential equations (Equations of the first order. Equations of higher order. Linear differential equations. System of linear equations of the first order. Differential equation of geodetic lines. The only differential equation of the second order geodesic lines).

1. Пискунов Н. С. Дифференциальное и интегральное исчисления: Учеб. для втузов. В 2-х т. Т.1: - М.: Интеграл-Пресс, 2001. – 416 с.
2. Пискунов Н. С. Дифференциальное и интегральное исчисления: Учеб. для втузов. В 2-х т. Т.2:- М.: Интеграл-Пресс, 2004. – 544 с.
3. Кудрявцев Л.Д., Математический анализ, т. 1,2. М. Наука,1988.
4. Шкіль М.І., Колесник Т.В. Вища математика. – К. Вища школа, 1986.
5. Мишкис А.Д. Лекции по высшей математике. М.: Наука, 1969. – 640с.

• Work on practical exercises, verbal questioning, written tests (30%).
• Final test (70%, inspections, and exam): written-verbal form (70%)