Jun 18, 2019   9:49 a.m. Vratislav

# 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:
 lecture 2 hours weekly (on-site method) seminar 4 hours weekly (on-site method)

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

Basic:
 ŠABO, M. Matematika I. STU v Bratislave, 2009. JASEM, M. -- HORANSKÁ, Ľ. Matematika I, Zbierka úloh. Bratislava : STU v Bratislave, 2009. 134 p. ISBN 978-80-227-3136-2.

Language of instruction: slovak or english

Notes:

Courses evaluation:
Assessed students in total: 1889

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5,6 %9,9 %13,4 %18,7 %31,2 %21,2 %
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.

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