Knowledge of:

1. The basic concepts and methods of linear and vector algebra.
2. The equation of a straight line in space, a plane, a sphere, an ellipse. Equation of a straight line on a plane, a circle, an ellipse, a hyperbola. Methods of solving typical problems of analytical geometry in space and on the plane.
3. The concept of a function of one and many variables. Properties of basic elementary functions. Concept of border and continuity.
4. Methods of differential calculus and its application for the study of functions, approximate calculations, and determination of parameters of functional dependence based on empirical data.
5. The concept of indefinite, definite, improper, multiple, curvilinear integrals. Methods of analytical and numerical integration of functions.
6. Fundamentals of the theory of differential equations. Analytical and numerical methods of solving differential equations.
7. Signs of convergence of numerical series. Concept of functional series and area of convergence. Properties of power and Fourier series.
8. The concept of random events and random variables. Numerical characteristics of random variables, basic laws of distribution. Methods of statistical processing of observation data, sample and interval evaluations, and testing of statistical hypotheses.

Skill:

1. Perform operations on matrices, and solve systems of linear algebraic equations.
2. Perform operations on vectors and solve basic problems of vector algebra.
3. To solve typical problems of analytical geometry in space and on the plane.
4. Calculate the limits of functions, and determine intervals of continuity.
5. Calculate derivatives and differentials of explicitly, implicitly and parametrically given functions.
6. Investigate functions using the methods of differential calculus. Approximate functions according to the formulas of Taylor and Maclaurin, determine parameters of functional dependence by the method of least squares.
7. Calculate indefinite, definite, curvilinear, multiple integrals. Determine areas, volumes, moments of inertia, and coordinates of the mass center using integrals.
8. Solve the simplest differential equations of the first order, linear differential equations with constant coefficients, and linear systems of differential equations.
9. Investigate series for convergence. Expand functions into power and trigonometric series. Apply series for approximate calculations.
10. To calculate the probabilities of events. Calculate numerical characteristics of random events.
11. Carry out selective estimates of distribution parameters, and build and test hypotheses about the distribution of a random variable based on statistical samples.

• Linear and Vector Algebra
• Analytic Geometry
• Introduction to Calculus
• Differential Calculus
• Integration Calculus
• Ordinary Differential Equations
• Numerical and Functional Series
• Probability Theory