1. Real functions of one real variable. Definition, graph. Bounded function, monotonic functions, even, odd and periodic functions. One-to-one functions, inverse and composite functions.
2. Limit of a function, improper limit of a function. Limit at an improper point. Continuous and discontinuous functions.
3. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules. Derivative of elementary functions.
4. l’Hospital rule.
5. Differential of a function. Derivatives of higher orders.
6. Relation between derivative and monotonicity, convexity and concavity of a function.
7. Extrema of a function. Asymptotes. Plot graph of a function.
8. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse matrix.
9. Determinants, properties of determinants.
10. Solution of systems of linear equations. Frobenius theorem. Gaussian elimination algorithm. Cramer’s rule.
11. Analytic geometry. Euclidean space. Scalar, vector and triple product of vectors, properties.
12. Equation of a plane, line in E3. Relative position problems.
13. Distance problems.
2. Limit of a function, improper limit of a function. Limit at an improper point. Continuous and discontinuous functions.
3. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules. Derivative of elementary functions.
4. l’Hospital rule.
5. Differential of a function. Derivatives of higher orders.
6. Relation between derivative and monotonicity, convexity and concavity of a function.
7. Extrema of a function. Asymptotes. Plot graph of a function.
8. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse matrix.
9. Determinants, properties of determinants.
10. Solution of systems of linear equations. Frobenius theorem. Gaussian elimination algorithm. Cramer’s rule.
11. Analytic geometry. Euclidean space. Scalar, vector and triple product of vectors, properties.
12. Equation of a plane, line in E3. Relative position problems.
13. Distance problems.