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ÚSI-ESMATAcad. year: 2023/2024
Basic mathematical concepts. Differential calculus of one variable, limit, continuity, derivative of a function. Derivatives of higher orders, l´Hospital rule, behavior of a function. Integral calculus of fuctions of one variable, indefinite integral. Integration by parts, substitution methods. Definite integral and its applications. Introduction to descriptive statistics. Introduction to probability, conditional probability, dependence and independence of random events. Total probability rule and Bayes theorem. Discrete random variables (probability mass function, cumulative distribution function, mean and variance). Discrete probability distributions (binomial, hypergeometric, Poisson, uniform). Continuous random variables (probability density function, distrubution function, mean, variance, quantiles). Exponencial distribution. Normal distribution. Central limit theorem. Testing of statistical hypotheses (t-test).
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Class attendance. If students are absent due to medical reasons, they should contact their lecturer.
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Syllabus
1. Basic mathematical concepts. High school math summary.2. Concept of a function (basic properties and graphs). Operations with functions.3. Differential calculus of one variable, limit, continuity.4. Derivative of a function. Derivatives of higher orders.5. l´Hospital rule. Behavior of a function, extremes.6. Integral calculus of fuctions of one variable, indefinite integral. Integration by parts, substitution methods.7. Definite integral and its applications.8. Introduction to descriptive statistics.9. Introduction to probability. Some probability models (classical, discrete, geometrical), conditional probability, dependence and independence of random events. Total probability rule and Bayes theorem. 10. Discrete random variables (probability mass function, cumulative distribution function, mean and variance). Discrete probability distributions (binomial, hypergeometric, Poisson, uniform). 11. Continuous random variables (probability density function, distrubution function, mean, variance). Exponencial distribution.12. Normal distribution. Central limit theorem.13. Testing of statistical hypotheses (t-test).
Computer-assisted exercise