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Lecturer(s)
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Schindler Martin, Mgr. Ph.D.
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Picek Jan, prof. RNDr. CSc.
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Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
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Slámová Tereza, Mgr. Ph.D.
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Course content
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Repetition of differential and integral calculus of functions of one variable. Differential calculus of functions of two or more variables: the concept of a function of n-variables, domain values??, graphs, partial derivatives. Local, global and constrained extrems. Integral calculus of functions of several variables: regions, the double integral and its properties, the calculation of double integrals (Fubini theorem). Matrix algebra, systems of linear equations. Probability - the basic properties and concepts: a random phenomenon, the definition of probability, conditional probability, independence of random events. Random variables: discrete random variable, continuous random variables, distribution functions, characteristics of random variables. Random Vector: distribution function, marginal distribution, independent random variables, conditional distribution, the characteristics of a random vector. Basic concepts of mathematical statistics: random sampling, point and interval estimation, consistency and unbiased estimate, basic hypothesis testing, analysis of variance. Linear regression model: the method of least squares, tests of regression parameters, regression diagnostics. Tests of two vectors of mean values ??(Hotelling tests). Methods of classification Discriminant analysis. Logistic regression. Cluster analysis
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 70 hours per semester
- Preparation for exam
- 110 hours per semester
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Learning outcomes
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Knowledge of calculus - multidimensional functions and knowledge of advanced methods of mathematical statistics and probability theory
Basic knowledge of calculus - functions of several variables, ability to apply advanced methods of mathematical statistics and probability theory
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Prerequisites
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Mathematics I (MV1) and Mathematics II (MV2) relevant Bachelor's degree
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Assessment methods and criteria
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Oral exam, Written exam
Requirements on credit: two tests of the subject matter. The date of each test will be announced in advance by teacher. It is necessary to get score at least 50% for each test. Requirements on exam: Knowledge of problem solving, concepts and basic ideas.
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Recommended literature
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Anděl, J. Statistické metody. Matfyzpress: Praha, 2007. ISBN 978-80-7378-003-6.
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Hebák, P., Hustopecký, J., Malá, I. Vícerozměrné statistické metody (2). Informatorium, Praha, 2005. ISBN 80-7333-036-9.
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Meloun M., Militký J. Statistická analýza experimentálních dat. Praha : Academia, 2004. ISBN 80-200-1254-0.
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Mezník, I. , Karásek, J., Miklíček, J.:. Matematika I pro strojní fakulty. SNTL, Praha, 1992.
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