26 hod., optionally

1. Real function of one real variable, explicit and parametric definition of a function. Composite function and inverse to a function. 2. Some elementary functions, inverse trigonometric functions. Hyperbolic functions. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real numbers. 3. Rational functions. Sequence and its limit. 4. Limit of a function, continuous functions, basic theorems. Derivative of a function, its geometric and physical applications, differentiating rules. 5. Derivatives of composite and inverse functions. Differential of a function. Rolle and Lagrange theorem. 6. Higher-order derivatives, higher-order differentials. Taylor theorem. 7. L`Hospital's rule. Asymptotes of the graph of a function. Sketching the graph of a function. 8. Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix. Solutions to systems of linear algebraic equations by Gauss elimination method. 9. Second-order determinants. Higher-order determinants calculated by Laplace expansion. Rules for calculating with determinants. Cramer's rule of solving a system of linear algebraic equations. 10. Inverse to a matrix. Jordan's method of calculation. Matrix equations. Real linear space, base and dimension of a linear space. Linear spaces of arithmetic and geometric vectors. 11. Eigenvalues and eigenvectors of a matrix. Coordinates of a vector. Dot and cross product of vectors, calculating with coordinates. 12. Mixed product of vectors. Plane and straight line in 3D, positional problems. 13. Metric problems. Surfaces.