Syllabus
Real numbers and their relation to rationals, complex numbers.
Sequences of real numbers: Basic properties of limit, bulk points, liminf and limsup. (Bolzano-Weierstrass theorem, limits of monotone sequences, etc.)
Informative series of real numbers.
Basic properties of functions (monotonicity, convexity, ...), definition by a series, basic approximations.
Function limits: methods of calculation.
Continuity of functions: extreme value theorem, intermediate value theorem.
Derivatives of functions: methods of calculation, usage - l'Hospital's rule, mean-value theorem, graphing a function. Taylor's polynomial.
Introduction to integral calculus: Newton integral (and methods of calculation), Riemann integral, applications (areas, volumes, lengths, estimates of sums).
Annotation
The first part of the mathematical analysis course for students of computer science, an introduction to the continuous world description, especially one-dimensional.
Students will learn to compute limits of sequences and functions, to determine and to use continuity of functions, to calculate and to use derivatives and also the basics of integral calculus - all for the functions of one variable.
In 2019/20, the course is being taught in both semesters. The winter semester variant is offered to students who started their studies in 2018/19, or earlier. In the summer edition, the