OGD19MAT2 - Matematika 2

Course specification
Type of study Bachelor academic studies
Study programme
Course title
Acronym Status Semester Number of classes ECTS
OGD19MAT2 mandatory 1 3L + 3E 7.0
Lecturer/Associate (practicals)
Prerequisite Form of prerequisites
No /
Learning objectives
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.
Learning outcomes
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.
Teaching Methods
Lectures and exercises
  1. Zoran Mitrović, Matematička analiza 1, ETF, Banja Luka, 2012. (Original title)
  2. Zoran Mitrović, Snježana Maksimović, Zbirka riješenih ispitnih zadataka iz matematičke analize 1, ETF, Banja Luka, 2014. (Original title)
Evaluation and grading
Class activity 5 points, Class attendance 5 points, Colloquium 1 30 points Colloquium 2, 30 points, Final exam 30 points
Specific remarks