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### Mathematical analysis 1

 Code: 21498 ECTS: 8.0 Lecturers in charge: izv. prof. dr. sc. Vjekoslav Kovač - Lectures prof. dr. sc. Hrvoje Šikić - Lectures Lecturers: doc. dr. sc. Igor Ciganović - Exercises Tomislav Kralj - Exercises doc. dr. sc. Snježana Lubura Strunjak - Exercises Mateo Tomašević, mag. math. - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
Lectures 45
Exercises 60
Description:
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.
Literature:
1. S. Kurepa: Matematička analiza 1: Diferenciranje i integriranje
2. S. Kurepa: Matematička analiza 2: Funkcije jedne varijable
3. M. H. Protter, C. B. Morrey: A First Course in Real Analysis
 1. semester Mandatory course - Regular study - Mathematics
Consultations schedule: