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, supremum and infimum, consequences of the continuity axiom, Bernoulli's inequality, intervals. The concept of sequence, boundary value, convergence criteria, theorem on algebraic combination of limes. More important limes, number e. Concept of real function of one variable, natural domain, zeros, sign, monotonicity, boundedness, parity and periodicity, composition of functions and inverse function, graph of functions. Basic elementary functions . The limit value of the function, more important limes, definite and indefinite forms of the limes of the function. Continuity of function. Properties of continuous functions. Even continuity. Concept of derivative, rules of derivation, table of derivatives, logarithmic derivative. Basic theorems of differential calculus (mean value theorems), Lopital's rule, monotonicity and extrema, asymptotes. The differential of the function,
Derivatives and differentials of higher order, Taylor's and McCloren's Convexity, graph drawing. Concept of indefinite integral, properties, table, direct integration, method
shifts. Method of partial inversion, integration of rational functions, integration of some irrational functions, Euler shifts. Integration of trigonometric functions, integral of the binomial differential.

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