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. Elementary functions (including inverse trigonometric functions).
3. Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions.
4. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules.
5. Derivative of elementary functions.
6. Differential of a function. Derivative of higher orders. l’Hospital rule.
7. Relation between derivative and monotonicity, convexity and concavity of a function.
8. Extrema of a function. Asymptotes. Plot graph of a function.
9. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse.
10. Determinants, properties of a determinant.
11. Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm.
12. Analytic geometry. Euclidean space. Scalar, cross and triple product of vectors, properties.
13. Equation of a plane, line in E3. Relative position problems.
14. Metric or distance problems.
2. Elementary functions (including inverse trigonometric functions).
3. Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions.
4. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules.
5. Derivative of elementary functions.
6. Differential of a function. Derivative of higher orders. l’Hospital rule.
7. Relation between derivative and monotonicity, convexity and concavity of a function.
8. Extrema of a function. Asymptotes. Plot graph of a function.
9. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse.
10. Determinants, properties of a determinant.
11. Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm.
12. Analytic geometry. Euclidean space. Scalar, cross and triple product of vectors, properties.
13. Equation of a plane, line in E3. Relative position problems.
14. Metric or distance problems.