# Course syllabus 42709_4B - Mathematics I (FCFT - WS 2017/2018)

**Information sheet**ECTS Syllabus

Slovak

**English**

University: | Slovak University of Technology in Bratislava | ||||||||||||

Faculty: | Faculty of Chemical and Food Technology | ||||||||||||

Course unit code: | 42709_4B | ||||||||||||

Course unit title: | Mathematics I | ||||||||||||

Mode of delivery, planned learning activities and teaching methods: | |||||||||||||

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Credits allocated: | 7 | ||||||||||||

Recommended semester/trimester: | -- item not defined -- | ||||||||||||

Level of study: | 1. | ||||||||||||

Prerequisites for registration: | none | ||||||||||||

Assesment methods: | |||||||||||||

Tests | |||||||||||||

Learning outcomes of the course unit: | |||||||||||||

Introduction to linear algebra, diferential and integral calculus | |||||||||||||

Course contents: | |||||||||||||

Linear vector space
Linear dependence and linear independence of vectors, dimension of a linear vector space. Matrices and basic properties of matrices Inverse matrix. System of linear equations. Polynomials. Real functions of one variable and their properties. Sequences, limit of a sequence Limit and continuity of a function. Cyclometric functions. Derivative of a functions. Derivative of a composite and an inverse function. Derivative of a higher order, differential L' Hospital's rule, Lagrange' s Theorem. Properties of functions having derivatives, graphing of functions Antiderivative -- primitive function, indefinite integral. Integration by substitution and by parts. Decomposition of rational functions into partial functions, Integration of rational functions Definite integral. Basic properties of definite integral. Mean -- value theorem for integrals, definite integral as a function of the upper limit. Computation of definite integral by substitution and by parts. Geometrical and physical applications of definite integral | |||||||||||||

Recommended or required reading: | |||||||||||||

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Language of instruction: | slovak or english | ||||||||||||

Notes: | |||||||||||||

Courses evaluation: | |||||||||||||

Assessed students in total: 1889
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Name of lecturer(s): | doc. RNDr. Vladimír Baláž, CSc. (examiner, instructor, lecturer) - slovak, english Mgr. Ľubomíra Horanská, PhD. (examiner, instructor, lecturer) - slovak, english doc. RNDr. Milan Jasem, CSc. (examiner, instructor, lecturer, person responsible for course) - slovak, english PaedDr. Tomáš Visnyai, PhD. (examiner, instructor, lecturer) | ||||||||||||

Last modification: | 22. 9. 2017 | ||||||||||||

Supervisor: | doc. RNDr. Milan Jasem, CSc. and programme supervisor |

*Last modification made by Ing. Tomáš Molnár on 09/22/2017.*