Course detail

Practicum in Mathematics 2

FP-pmlPAcad. year: 2024/2025

The content of this practicum corresponds to the subject Mathematics 2 and provides students with the opportunity to become more familiar with the practical resolution of specific problems, practice more difficult topics, and overcome challenges in mastering the material.

Requirements for Course Credit:

Passing control tests and achieving at least 50% of the points.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. RNDr. Bedřich Půža, CSc.

Department

Institute of Informatics (ÚI)

Entry knowledge

High school mathematics and the subject Mathematics I.

Rules for evaluation and completion of the course

Requirements for Course Credit:

Passing control tests and achieving at least 50% of the points.

Attendance at the practicum sessions is monitored.




Aims

The aim of the course is to review, reinforce, and organize the knowledge acquired in the lectures and exercises for the subject Mathematics II, and to develop students' skills in independently solving problems from all the covered thematic areas. Students will understand and be able to solve selected applications of mathematics in economics and informatics. Students will be introduced to both Czech and English technical terminology.

The acquired knowledge and practical mathematical skills will primarily support gaining knowledge and expanding skills in economically oriented fields and for the correct use of mathematical software. Additionally, they will serve as an important foundation for acquiring new insights in related mathematical subjects.



Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

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

Classification of course in study plans

  • Programme BAK-EP Bachelor's 1 year of study, summer semester, elective
  • Programme BAK-MIn Bachelor's 1 year of study, summer semester, elective
  • Programme BAK-UAD Bachelor's 1 year of study, summer semester, elective
  • Programme BAK-PM Bachelor's 1 year of study, summer semester, elective

Type of course unit

 

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Bedřich Půža, CSc.

Syllabus

  1. Series of Numbers (necessary condition for convergence, basic criteria for convergence and divergence of series, estimation of the remainder)

  2. Power Series (construction of Taylor polynomial and estimation of the remainder, Taylor's formula for approximate calculation of function values and integrals)

  3. Indefinite Integral (application of properties and basic rules for calculating integrals)

  4. Integration Methods (application of integration by parts and substitution methods, integration of simple rational functions)

  5. Definite Integral (use of properties and basic rules for calculation, additional applications, convergence and, if applicable, calculation of improper integrals)

  6. Ordinary Differential Equations (general and particular solutions of equations with separated variables)

  7. Linear First-Order Differential Equations (solutions of homogeneous and non-homogeneous equations, method of variation of constants)

  8. Functions of Two Variables I (domains of definition, graphs of simpler functions of 2 variables and their sections, continuity disruptions, calculations of first-order partial derivatives)

  9. Functions of Two Variables II (calculations of higher-order partial derivatives, determination of gradient and Hessian matrix of functions of 2 variables)

  10. Extrema of Functions of Two Variables (calculation of stationary points and determination of their nature – local extremum, determination of absolute and constrained extrema – Lagrange method)

  11. Mathematical Logic (working with propositions and operations on them, laws and rules)

  12. Relations (determination of properties of relations between sets and within a set)

  13. Graphs (classification of graphs, determination of the shortest path in a weighted (directed) graph)