1. Introduction to mathematical logic, statements, quantifiers, negation, logical structure of mathematics, proofs of mathematical theorems. 2. Sets, relationship between sets, set operations, Cartesian product of sets, mapping, number sets. 3. Intervals, neighbourhood of a point, properties of a subsets of set of real numbers, relationship between a set and a point. 4. Sequences  definition, properties, algebraic operations with sequences. 5. Limit of a sequence  definition, properties. 6. Limit of a sequence  properties and calculation. 7. Function of a single real variable  definition, properties. 8. Function of a single variable  properties, algebraic operations with functions, function composition, inverse function. 9. Limit of a function  motivation, definition. 10. Limit of a function  properties, onesided limits. 11. Limit of a function  calculation. Function continuity  definition, properties. 12. Points of discontinuity, functions continuous on a set, function continuous on a closed interval. 13. Differentiation of a function at a point  definition, tangent line and normal line, differentiation of a function on a set. 14. Calculation of derivatives, higher derivatives, the interpretation of the second derivative. 15. Elementary theorems of differential calculus. 16. Approximation of a function  differential, Taylor polynomial. 17. The application of differential calculus  analysing properties of a function  part I. 18. The application of differential calculus  analysing properties of a function  part II 19. Indefinite integral  primitive functions, calculation of primitive function. 20. Indefinite integral  integration of rational functions. 21. Indefinite integral  special substitutions. 22. Riemann integral  motivation, definition. 23. Riemann integral  conditions of integrability, properties. 24. Riemann integral  calculation, application.


B. P. Děmidovič. (2003). Sbírka úloh a cvičení z matematické analýzy. Fragment, Praha.

Bartsch, H.J. (1983). Matematické vzorce. Praha: SNTL.

J. Brabec, F. Martan, Z. Rozenský. (1989). Matematická analýza I. Praha: SNTL.

K. Rektorys. (1963). Přehled užité matematiky. SNTL Praha.

V. Mádrová, J. Marek. (2004). Řešené příklady a cvičení z matematické analýzy I. VUP Olomouc.

V. Mádrová. (2004). Matematická analýza I. VUP, Olomouc.
