Content (Syllabus outline)
· Selected topics in calculus: characteristics of real numbers, linear, quadratic, exponential and logarithmic equations; properties of sequences and series, limits of sequences, definition of number e; simple interest, compound interest, annuities, present value of annuity, law of natural growth.
· Functions of one real variable: properties and graphs of linear, quadratic, rational, exponential, logarithmic, trigonometric functions, 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.
· Elementary linear algebra: determinants, multiplication of matrices, inverse of a matrix, 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, pollution problems), the use of software for solving agricultural/animal production cases.
· 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.
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, computer programs and spreadsheets.
Prerequisites
Conditions for inclusion in the work:
Enrolment in the appropriate academic year.
Conditions for performing study obligations
Prerequisite for permission to attend the final exam:
- Attendance at tutorials
- written examination from tutorial
- Exam (written examination)