Mathematics

Course Coordinator

ECTS points:
6

Program:
preddiplomski

Course number:
32167

Course Description

COURSE CONTENT

  • Notions related to real functions of one variable. Boundedness of sets and functions. The notion of inverse functions and criteria for their existence. Arcus functions.
  • Function continuity and limits. The number e. Important limits
  • The problem of tangent and velocity. The notion of a function derivative. Table of elementary derivatives. Basic properties. Higher order derivatives
  • Diferentials and their application. Five elementary theorems of differential calculus. Characterization of monotonicity and convexity/concavity. Characterization of local extrema and inflection points. L’Hospital’s rule. Asymptotes. Qualitative graph of a function
  • Matrix algebra. Determinant of a matrix. Properties. Inverse matrix, its existence and construction. Linear systems
  • The problem of area calculation and construction of the definite integral. Properties. Integral mean value theorem
  • Newton-Leibniz formula. Substitution and integration by parts in the definite integral
  • Application of the definite integral. Area of planar figures and volume of rotational bodies
  • Elementary models of first order differential equations

LEARNING OUTCOMES

  • recognize and outline graphs of elementary functions, determine domains of more complex functions
  • calculate limit values of functions, and recognize functions related to the number e
  • calculate function derivatives and determine approximate values of functions
  • apply differential calculus in analyzing properties of functions and their graphs
  • solve matrix equations and solve systems of linear equations by using the Gauss algorithm
  • utilize basic integration techniques and relate the notions of definite and indefinite integral
  • recognize ways in which the definite integral arises
  • apply integral calculus to calculate areas and volumes of rotational bodies
  • solve first order differential equations and recognize basic models of differential equations