1. komponenta

Lecture type	Total
Lectures	60
Exercises	45

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

COURSE AIMS AND OBJECTIVES: The main objective of the course is to familiarize students with the foundations of differential and integral calculus in one dimension. More precisely, the course studies derivatives, integrals, and series. The teaching method combines rigorous proof and operational techniques through examples, encouraging the student to acquire both skills at the same time.

COURSE DESCRIPTION AND SYLLABUS:
1. Derivatives. Motivation (geometric, physical) and definition of the derivative, relationship between differentiability and continuity, basic rules for differentiation, derivatives of elementary functions. Rolle's and Lagrange's mean value theorems, monotonicity, local extrema. Higher-order derivatives, Taylor's mean value theorem, convexity, inflection. Asymptotes, analysis of the behavior and graph of a function. Applications. (5 weeks)
2. Integrals. Motivation (area, work done by a force) and definition of the Riemann integral. Integrability of monotone and (piecewise) continuous functions. Antiderivative, Newton-Leibniz formula. Substitution, integration by parts, integration of rational functions. Improper integrals. (5 weeks)
3. Series. Definition, convergence tests. Power series, Taylor series. Uniform convergence, series of functions. (3 weeks)

1. Matematička analiza 1 & 2, skripta, B. Guljaš.
2. Matematička analiza 1, S. Kurepa, Školska knjiga, Zagreb, 1997.
3. Mathematical Analysis 1, V. Zorich, Springer Verlag, Berlin, 2015.
4. Introduction to Real Analysis, R. G. Bartle, D. R. Sherbert, John Wiley & Sons, 2011.
5. Analysis I, T. Tao, Hindustan Book Agency & Springer, 2022.

Enrollment :
Attended : Mathematical analysis 1

Examination :
Passed : Mathematical analysis 1

Mandatory course - Regular study - Mathematics