# Mathematics 2

## Associates

 ECTS points: 5 Program:preddiplomski Course number: 24094; 24119; 239337; 239475

## 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
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