1. komponenta

Lecture type	Total
Lectures	45
Exercises	60

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: The goal of the course is to introduce the basics of mathematical analysis in the set of real numbers.

COURSE DESCRIPTION AND SYLLABUS:
1. Introduction. Sets N, Z, Q, operations and order, geometric interpretation on real axis, proof that , motivation for R. Notion of function, Cartesian coordinates, graph of a real function of real variable, affine functions, simple rational functions. Quadratic function, polynomials, rational functions, composition of functions, injectivity, surjectivity, bijectivity, inverse function. Roots, exponential function on Q, logarithmic function, hyperbolic and area functions. Trigonometric functions (geometric definition on unit circle), arcus functions, solving equations containing trigonometric and exponential functions. Axioms of real field R, supremum and infimum of a set, completeness. (6 weeks)
2. Sequences. Notion of sequence and subsequence, monotony, boundednes, monotonic subsequence, various examples of sequences. Convergence, basic rules, connection between convergence, boundednes and monotony, Cauchy sequence, limes superior and limes inferior. Field C, sequences in C, convergence in C and by coordinates. (3 weeks)
3. Continuity. Limit of function and basic rules, continuity of function and operations with continuous functions, continuity of rational functions. Strict definition of exponential function, continuity of exponential function. Correspondence between continuity, boundednes and monotony, continuity of inverse function. Continuity of elementary functions.

Mandatory course - Regular study - Mathematics