Mathematics 2

Course Coordinator

ECTS points:
5

Program:
preddiplomski

Course number:
24094; 24119

Course Description

COURSE CONTENT

  • Problem of area calculation and connection with the definite integral
  • Properties of the definite integral
  • The notions of primitive function and indefinite integral. Direct integration
  • The methods of substitution and integration by parts
  • Integration of some classes of functions (rational functions, trigonometric expression, irrational expressions)
  • 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, arc length, volume of rotational bodies
  • Vectors in space. Linear combinations and linear independence
  • Scalar and vector products of vectors. Application
  • Planes and lines in space
  • Higher-order partial derivatives. Schwarz’s theorem
  • Differentials and approximation
  • Local extrema and optimization problems
  • Differentiation of compounded multi-variable functions. Chain rule
  • Ordinary differential equations of the first order. Separation of variables
  • Homogenous differential equations
  • Linear and Bernoulli’s differential equation. Exact differential equations
  • Order reduction for some second order differential equations
  • Linear differential equations of the second order with constant coefficients

LEARNING OUTCOMES

  • use elementary methods of integral calculus, and relate the notion of the definite and indefinite integral
  • recognize ways in which the definite integral arises
  • apply integral calculus in calculation of area, arc length and volume
  • calculate partial derivatives and approximate function value by using differentials
  • apply differential calculus in various optimization problems
  • solve first and second order differential equations and recognize basic models of differential equations