Content (Syllabus outline)
· Sets and numbers: relations with sets, real numbers (linear, quadratic, exponential and logarithmic equations, absolute values, intervals), definition of complex numbers.
· Sequences, series and financial mathematics: definition and properties of sequences and series, limits of sequences, arithmetic progressions, geometric progressions, infinite geometric series, definition of number e, simple interest, compound interest, annuities, present value of annuity, law of natural growth.
· Functions of one real variable: definition of functions and their graphs, linear, quadratic, rational, exponential, logarithmic, trigonometric functions and their properties, continuity and limits.
· Derivatives: the derivative, tangent to a curve, derivative formulas, higher order derivatives, relative minima and maxima, concavity, convexity, points of inflection, elasticity, elasticity of demand.
· Functions of two real variables: partial differentiation, higher order partial derivatives, maxima and minima, least squares method.
· Integrals: definition of indefinite integrals, basic integration formulas, definition of the definite integral, properties and calculation of definite integrals, improper integrals.
· Matrices and system of linear equations: determinants, matrix algebra, multiplication of matrices, inverse of a matrix, rank of a matrix, system of linear equations, Gauss-Jordan elimination, vectors, calculations of scalar, vector and scalar triple products.
Probability: permutations, variations and combinations, definition of probability. Bernoulli’s formula, discrete probability distributions, binomial and Poisson distribution, continuous distribution, normal distribution, calculation of mean and variance of discrete and continuous distributed random variables.
Prerequisites
1. Prerequisite for course work:
Enrolment in the corresponding (1st) year of the study program
2. Prerequisite for permission to attend the final exam:
- Attendance at tutorials