1. Functions of one real variable (definitions and basic properties).
2. Elementary functions. Parametric and implicit functions.
3. Limit of the function, continuous functions. Definition of the derivative.
4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
6-8. Applications of the derivatives. Tangent line, Taylor polynomial, extremes of a function. Behaviour of the graph. Monotonic functions. Convex and concave functions. Inverse functions. Computation of limits by l'Hospital rule. Asymptotes.
9. Systems of linear equations, Gaussian elimination
10. Matrices, rank of a matrix. Matrix inversion
11. Determinant, its computation and properties. Cramer rule.
12. Analytic geometry in Euclidean space. Dot product and cross product
13. Line and plane in 3D-Euclidean space.
14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.
2. Elementary functions. Parametric and implicit functions.
3. Limit of the function, continuous functions. Definition of the derivative.
4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
6-8. Applications of the derivatives. Tangent line, Taylor polynomial, extremes of a function. Behaviour of the graph. Monotonic functions. Convex and concave functions. Inverse functions. Computation of limits by l'Hospital rule. Asymptotes.
9. Systems of linear equations, Gaussian elimination
10. Matrices, rank of a matrix. Matrix inversion
11. Determinant, its computation and properties. Cramer rule.
12. Analytic geometry in Euclidean space. Dot product and cross product
13. Line and plane in 3D-Euclidean space.
14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.