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. Mgr. Veronika Novotná, Ph.D.

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 granting credit:
Passing control tests and achieving at least 50% points.

Requirements for granting credit for students with ISP:
Passing control tests and achieving at least 50% points.




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. András Rontó
RNDr. Zuzana Chvátalová, Ph.D.

Syllabus

  1. 1. Review of the 1st semester - working with functions
    2. Review of the 1st semester - derivatives, applications of derivatives
    3. Function course I (monotonicity, local and absolute extrema of a function, convexity and concavity)
    4. Function course II (asymptotes of a function, complete description of the behavior of a function)
    5. Indefinite integral (meaning, properties, basic rules for calculation)
    6. Integration methods I (method per partes and substitution)
    7. Integration methods II (decomposition into partial fractions, integration of rational fractional functions)
    8. Definite integral (meaning, properties, rules for calculation)
    9. Definite integral (applications)
    10. Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)
    11. Extrema of functions of several variables (partial derivatives of higher orders, local and on compact sets extrema)
    12. Bound extrema (Lagrange's method)
    13. 1st order differential equations with separated variables