In this course, students are introduced to elementary functions and their properties. Special attention is focused on the graph of an arbitrary function, the boundary values ​​of functions, the concept of derivatives and integrals.

By studying this subject, students acquire knowledge of elementary functions and their properties, as well as the technique of derivation and integration.

Axioms of the set of real numbers, intervals, supremum and infimum of the set.. Real functions of one variable. Basic elementary functions. The concept of a series and the limit value of a series. Monotonicity and sequence boundedness. Some important limes. Number e. Limit value (limes) of the function, definite and indefinite forms of the limes of the function. Continuity of function. The first derivative and its geometric interpretation. Differentiation rules. Differential of a function. Theorems on mean values ​​of differential calculus. Monotonicity and extreme values ​​of the function. Lopital's rule. Derivatives of higher order, convexity . Taylor's and MacLauren's formula. Asymptotes of functions. Graphing a function. The concept of indefinite integral, properties, direct integration. Shift method, partial entry method. Integration of rational functions, integration of some irrational functions, integration of trigonometric functions.
The concept of definite integral and properties. Newton-Leibnitz formula. Improper integral. Application of the definite integral.

1. Zoran Mitrović, Matematička analiza 1, ETF, Banja Luka, 2012.

   (Original)

2. Zoran Mitrović, Snježana Maksimović, Zbirka riješenih ispitnih zadataka iz matematičke analize 1, ETF, Banja Luka, 2014.

   (Original)

Class activity 5 points, Class attendance 5 points, Colloquium 1 30 points Colloquium 2, 30 points, Final exam 30 points

Lectures and exercises