1. Real function of one real variable. Operations with functions. (Basic) elementary functions.
2. Properties of functions - intersections with axes, sign of function, boundary, monotonicity, extremes, convexity, concavity, parity, simplicity, invertibility, periodicity.
3. Limit of a function, limit theorems, asmyptotes to a function graph.
4. Continuity and discontinuity of function.
5. Derivative of function - geometric and physical meaning. Derivative of basic elementary functions. Differentiation rules. Derivatives of higher orders.
6. Use of derivatives - L'Hospital rule, basic theorems of differential calculus, analysis of the course of a function.
7. Function differential, Taylor polynomial.
8. Arithmetic vector space. Linear independence vectors.
9. Matrices - types, special matrices, operations.
10. Determinant. Inverse matrix. Rank.
11. Systems of linear equations. Frobenius theorem. Gaussian elimination method. Cramer rule.
12. Line and plane in Euclidean space. Scalar, vector and mixed product of vectors.
13. Line and plane equations in E3 and their relative positions, distances and deviations of basic objects in E3.
2. Properties of functions - intersections with axes, sign of function, boundary, monotonicity, extremes, convexity, concavity, parity, simplicity, invertibility, periodicity.
3. Limit of a function, limit theorems, asmyptotes to a function graph.
4. Continuity and discontinuity of function.
5. Derivative of function - geometric and physical meaning. Derivative of basic elementary functions. Differentiation rules. Derivatives of higher orders.
6. Use of derivatives - L'Hospital rule, basic theorems of differential calculus, analysis of the course of a function.
7. Function differential, Taylor polynomial.
8. Arithmetic vector space. Linear independence vectors.
9. Matrices - types, special matrices, operations.
10. Determinant. Inverse matrix. Rank.
11. Systems of linear equations. Frobenius theorem. Gaussian elimination method. Cramer rule.
12. Line and plane in Euclidean space. Scalar, vector and mixed product of vectors.
13. Line and plane equations in E3 and their relative positions, distances and deviations of basic objects in E3.