Content (Syllabus outline)
- Elementary linear algebra: multiplication of matrices, inverse of a matrix, determinants, rank of a matrix, system of linear equations, systems of linear inequalities, definition of a linear program, a geometric approach to linear programming problems (production, diet, transportation problems).
- Introduction to decision making and network models: decision tree; decision making under uncertainty and risk, the value of complete information, network planning, graphical interpretation, shortest path.
- Functions of one real variable: properties and graphs of linear, quadratic, rational, exponential, logarithmic, trigonometric functions, linear, quadratic, exponential and logarithmic equations, continuity and limits, derivatives, relative and absolute minima and maxima, concavity, convexity, points of inflection, elasticity, elasticity of demand; indefinite integrals, basic integration formulas, definition of the definite integral, properties and calculation of definite integrals, some examples from the field of agriculture.
- Functions of two real variables: partial differentiation, higher order partial derivatives, maxima and minima, least squares method.
- Introduction to probability: permutations and combinations, trials, events, probabilities, mutually exclusive and non-exclusive events, dependent and independent events, compound events, conditional probability, Bernoulli’s formula, discrete random variables, binomial and Poisson distribution, continuous distribution, normal distribution.
- Vectors: their geometrical significance, linear dependence and independence of vectors, scalar, vector and scalar triple products, eigen values and eigen vectors
- Differential equations: differential equations with separable variables, linear differential equations of first order, examples
- Statistics: basic statistical concepts: tables, grouped data, frequency distribution, bar charts, pie diagrams, graphs, histogram, polygon, ogive, quartiles, deciles, percentiles, arithmetic mean, median, mode, standard deviation and some other measures of dispersion, introduction to correlation of two numerical variables, scatter diagram, regression line, coefficient of correlation, confidence intervals for the mean and proportion of population, sample size, hypothesis tests for one, two or more samples, parametric tests (z-test, t-test, F-test, Chi-square test), nonparametric tests, examples of professional practice and application of computer programs.
Prerequisites
1. Prerequisite for course work:
Enrolment in the corresponding (1st) year of the study program
2. Prerequisite to attend the final exam:
- Attendance at tutorials
- Fulfilled obligations from lectures and tutorials
Seminar