Course detail

Practicum in Mathematics for Informatics 2

FP-MpmlKAcad. year: 2020/2021

The content of this practice corresponds to the subject Mathematics 2 and gives students the opportunity to get acquainted with the practical solution of specific tasks, to practice the difficult parts and to overcome the difficulties in the management of the curriculum.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Learning outcomes of the course unit

The acquired knowledge and practical mathematical skills will in particular serve as a basis for acquiring knowledge and disseminating skills in economically oriented fields and for the correct use of mathematical software, and will be an important starting point for learning new knowledge in math mathematical subjects.

Prerequisites

Knowledge of secondary-school mathematics and successful completion of the course “Mathematics I”.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Practice is focused on practical calculations and application tasks.

Assesment methods and criteria linked to learning outcomes

Requirements for credit:
-active participation in exercises,
- fulfillment of individual tasks and written assignments,
- Absence of a control test during the semester with a rating of at least "sufficient" (E).

Course curriculum

1. Sequences (determination of basic properties of sequence of real numbers - limitation and monotony, calculation or estimation of sequence limit)
2. Derivatives of the 1st order (calculation of the function derivative using the general rules and the derivation of the elementary functions)
3. Derivatives of the first and higher orders (calculation of the differential and its use, calculating the higher order derivative, l'Hospitality rule)
4. Function I (determination of monotony intervals, calculation of local and absolute extremes of function)
5. Function II (determination of convexity, concavity and inflection points, calculation of function asymptotes, complete description of function behavior including sketch of its graph)
6. Indeterminate integral (use of properties and basic rules for integrals calculation)
7. Integration methods (using per partes and substitution methods, integration of simple rational functions)
8. Certain integral (use of properties and basic rules for calculation, other applications, convergence and possibly calculation of the integral integral)
9. Ordinary differential equations (general and specific solutions of equations with separated variables)
10. Linear differential equations of the first order (solution of homogeneous and inhomogeneous equation, method of constant variation)
11. Function of two variables I (definition domains, graphs of simple functions of 2 variables and its cuts, continuity disorders, calculations of partial derivations of first order)
12. Function of two variables II (calculations of higher order partial derivations, gradient determination and Hess matrix function of 2 variables)
13. Extremes of function of two variables (calculation of stationary points and determination of their character - local extreme, determination of absolute and bound extremes - Lagrange method)

Work placements

Not applicable.

Aims

Objective of the course in terms of learning outcomes and competences The aim of the subject is to repeat, consolidate and classify the knowledge gained in lectures and exercises in Mathematics II and to develop the students' ability to solve problems independently from all the topics covered. Students will understand and will be able to solve selected applications of mathematics in economics, respectively. information technology. Students will be acquainted with Czech and English terminology.

Specification of controlled education, way of implementation and compensation for absences

Within the exercises the students complete 10-minute written tests with the specification of the subject areas. To prepare for them, to evaluate the tests and consultations, e-learning is used in which students have their own
electronic materials available, including control-solved examples. The student is awarded a credit after successful completion (with at least 50% of successfully solved examples).

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

MEZNÍK, I. Diskrétní matematika pro užitou informatiku, Brno 2013, CERM s.r.o., 185 s, ISBN: 978-80-214-4761- 5
MEZNÍK, I.: Matematika I, , 9. vydání, Brno 2011, FP VUT v Brně, 150s, ISBN 978-80-214-3725-8
MEZNÍK, I.: Matematika II., 11.vydání, Brno 2009, CERM s.r.o., 105s, ISBN 978-80-214-3816-3
MAROŠOVÁ, M. - MEZNÍK, I.: Cvičení z matematiky I., 2. vydání, Brno 2008, FP VUT v Brně, 144s, ISBN 978-80-214-3724-1

Recommended reading

MEZNÍK, I.- KARÁSEK, J.- MIKLÍČEK, J.: Matematika I pro strojní fakulty, 1. vydání, SNTL, Praha 1992, 502s, ISBN 80–03–00313-X
FECENKO, J.: Matematika. 2.vydání, Ekonóm, Bratislava 1995, 377s, ISBN 80-225-0675-3
JACQUES, I.: Mathematics for economics and business. Second edition. Addison-Wesley, Wokingham 1994. 485s. ISBN 0-201-42769-9

Classification of course in study plans