Practise

In the 2026/2027 the midterm test will be written in the 10th week (the week since 23rd November 2026).

1. Sequence, limit of sequence – definition, limit of polynomials, quotients of polynomials.
2. Limits containing qⁿ. Limits with a parameter. Limits of a function – definition, limits from graphs, limits at non-eigenpoints, type a/0 (one-sided limits).
3. Limit of a composite function, continuity relation and limits, continuity theorem of elementary functions. Derivation – definition, geometric interpretation, basic rules and formulas, examples of mechanical differentiation.
4. Higher-order derivatives, Taylor polynomial, equation of the tangent to the graph of a function. Bolzano’s theorem.
5. L’Hospital’s rule – types 0/0, ∞/∞. The importance of the first derivative for the course of a function: determining the intervals in which the function is increasing, decreasing and has local extreme.
6. Weierstrass theorem, extrema of a continuous function on a function on a closed interval. Theorem on the importance of the second derivative for the course of a function: determination of intervals in which the function is convex, concave and inflection points.
7. Innovation Week (without scheduled classes).
8. Integrals – indefinite integral and primitive functions. Basic rules and formulas, per partes method (integral by parts).
9. Formula f´/f, substitution, definite integral (geometric meaning and calculation).
10. Midterm test
11. Area – between the graph of a function and the x-axis, between two functions. Improper integral.
12. Functions of two variables, compact set, domain of a function of two variables. Partial derivatives of the 1st and 2nd order, local extreme of a function of two variables.
13. Local bound extrema of a function of two variables (substitution method), bound extrema of a function of two variables (Jacobian).