Mathematics

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