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Sylabus předmětu B-MAT1 - Mathematics 1 (FEEIT - SS 2019/2020)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Electrical Engineering and Information Technology
Course unit title: Mathematics 1
Course unit code: B-MAT1
Mode of completion and Number of ECTS credits: Exam (6 credits)
 
Name of lecturer: doc. Mgr. Marcel Polakovič, PhD. (person responsible for course) - slovak
doc. RNDr. Michal Zajac, PhD. (examiner, instructor, lecturer) - slovak
 
Learning outcomes of the course unit:
Student will gain basic knowledege and skill in linear algebra (complex numbers, matrices, systems
of linear equations, determinants). He will get knowledge in the elements of elementary functions,
he will be able to solve some basic limits. He will learn the basics of differential calculus:
he will be able to count the derivatives of functions and apply them to some basic problems of
mathematical analysis (local extremes, convexity etc.) Finally, he will get knowledge in solution
of various problems about infinite series.
 
Prerequisites and co-requisites: none
 
Course contents:
Course contents

1. Linear algebra
a) real and complex numbers
b) matrices, elimination methods of solving of the systems of linear equations
c) determinants
d) sum and product of matrices, inverse matrix

2. Real functions
a) Definitions of a function, even and odd function, bounded function. Elementary functions.
b) limit and continuity of functions
c) differentiable functions, computing of derivatives

3. Using derivatives to investigate functions
a) asymptotes of the graph of a function
b) the Rolle and Lagrange theorem, monotone functions, local extremes
c) convex and concave functions

4. Sequences and series
a) convergent and divergent series, absolutely convergent series, geometric series
b) Cauchy, D'Alembert and Leibniz criteria of convergence
c) power series, the Taylor theorem and Taylor series

 
Recommended or required reading:
Basic:
GALANOVÁ, J. Lineárna algebra . Bratislava: STU Bratislava, 2002.
SABOLOVÁ, M. -- SATKO, L. Matematická analýza 1. Bratislava : STU v Bratislave, 2005. 61 p. ISBN 80-227-2269-3.
MARKO, Ľ. Matematická analýza online.  [online]. 2003. URL: http://aladin.elf.stuba.sk/~marko.
STROUD, K. Engineering Mathematics. Hong Kong: Macmillan Presss LTD, 1993.
ŠULKA, R. -- MORAVSKÝ, L. -- SATKO, L. Matematická analýza 1. Bratislava : Alfa, 1986. 389 p.

 
Planned learning activities and teaching methods: Each week, there will be two lectures, each by two hours and one seminar by two hours.
 
Assesment methods and criteria: seminars 40% - examination 60%
 
Language of instruction: Slovak, English
 
Work placement(s): There is no compulsory work placement in the course unit.


Last modification made by RNDr. Marian Puškár on 05/07/2019.

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