The subject is divided into four main parts. The first one is devoted to selected topics in algebra. The second part deals with real functions of one variable. The third part is devoted to differential calculus of functions of one variable. The final part deals with integral calculus of functions of one variable.
1. week: Notion of a vector, linear dependence and independence of vectors. Matrices. Properties of matrices. Operations with matrices.
2. week: Rank of a matrix. Systems of linear equations.
3. week: Determinants, definition and properties. Cramer's rule. Inverse of a matrix. Matrix equations.
4. week: Complex numbers. Polynomials and algebraic equations.
5. week: Real fuctions. Properties of real functions. Composite and inverse functions. Exponential and logarithmic function. Cyclometric functions.
6. week: Sequences. Limit of a sequence. Limit and continuity of a function.
7. week: Derivative of a function. Derivative of composite and inverse functions. Higher order derivatives. L' Hospital's rule. Differential.
8. week: Taylor polynomial. Properties of functions with a derivative. Asymptotes.
9. week: Indefinite integral, definition. Basic properties and formulas. Integration by substitution. Integration by parts.
10. week: Decomposition into partial fractions. Integration of rational and other functions.
11. week: Definite integral, definition and properties. Newton-Leibniz formula. The mean value theorem. Calculation methods.
12. week: Applications of definite integral. Planar area calculation.
13. week: Length of plane curves. Volume of rotating solids.