| Learning outcomes of course unit |
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- Knowledge of basic concepts and methods of linear and vector algebra.
- Equations of a straight line in space, planes. Equations of a straight line on a plane, circle, ellipse, hyperbola, parabola. Equations of cylindrical surfaces of the second order, surfaces of revolution, conical surfaces. Canonical equations of surfaces of the second order. Methods of solving typical problems of analytical geometry in space and on the plane.
- The concept of a function of one and many variables. Properties of basic elementary functions. Concept of limits and continuity of functionі.
- Methods of differential calculus and its application for the research of functions, approximate calculations, determination of parameters of functional dependence based on empirical data.
- The concept of indefinite, definite, improper, multiple, curvilinear integrals. Methods of analytical and numerical integration of functions.
- . Fundamentals of the theory of differential equations. Analytical and numerical methods of solving differential equations.
- Signs of convergence of numerical and functional series. Properties of power series.
- The concept of random event and random variable. Numerical characteristics of random variables, basic laws of distribution.
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- Perform operations on matrices, solve systems of linear algebraic equations. Perform operations on vectors and solve basic problems of vector algebra.
- To solve typical problems of analytical geometry in space and on the plane.
- Calculate the limits of functions, determine intervals of continuity.
- Calculate derivatives and differentials of explicitly, implicitly and parametrically given functions. Investigate functions by methods of differential calculus. Represent functions using Taylor Maclauren formulas. Determine parameters of functional dependence by the method of least squares.
- Calculate indefinite, definite, curvilinear, multiple integrals. Determine areas, volumes, moments of inertia, coordinates of the center of mass using integrals.
- Solve the simplest differential equations of the first order, linear differential equations with constant coefficients, linear systems of differential equations.
- Investigate series for convergence. Expand functions into power series. Apply series for approximate calculations.
- Calculate the probabilities of events. Calculate numerical characteristics of random variables. Carry out selective and interval estimations of distribution parameters. Propose and test hypotheses about the distribution of a random variable based on statistical samples.
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