Course detail

Mathematics 1

FP-ma1PAcad. year: 2025/2026

The subject is part of the theoretical basis of the field. Learning outcomes of the course unit The aim of the course is to unify and supplement the students' knowledge in the areas of further teaching of basic mathematical concepts and to teach students the comprehension of using the linear algebra system to solve the linear equations and the differential functions of one variable (including basic applications in economic disciplines).

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Knowledge of secondary-school mathematics.

Rules for evaluation and completion of the course

Requirements for awarding credit:

Passing control tests and achieving at least 55% of points or completing a comprehensive written paper and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam is written.

For all tasks in the written part, a calculation must be written, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory) and the student does not proceed to the oral part.

If the student does not achieve at least 50% of the total number of achievable points in the written paper, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory).

Completion of the course for students with individual study:
Passing the comprehensive control test and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.
The exam is written.
For all tasks in the written part, a calculation must be written, or the procedure described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory).
If the student does not achieve at least 50% of the total number of achievable points in the written work, the written part and the entire exam are graded "F".

Participation in seminars is checked.

Aims

Learning outcomes of the course unit The aim of the course is to solve systems of linear equations and detailed analysis of the processes described by the real function of one real variable, including the realization of necessary calculations in general and in economic applications (also with respect to the use of computing).
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.

Study aids

Viz. literature

Prerequisites and corequisites

Not applicable.

Basic literature

Marošová,M. - Mezník,I.: Cvičení z matematiky I. 2. vydání, FP VUT v Brně, Brno 2008 (CS)
MEZNÍK, I. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS) (CS)

Recommended reading

Not applicable.

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BAK-EP Bachelor's 1 year of study, winter semester, compulsory
  • Programme BAK-PM Bachelor's 1 year of study, winter semester, compulsory
  • Programme BAK-UAD Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

Mgr. Martina Bobalová, Ph.D.
doc. Mgr. Veronika Novotná, Ph.D.
doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Syllabus

1. Matrices (properties, matrix operations, rank calculation and inverse matrix)
2. Determinants (properties, rules and calculation of determinants)
3. Systems of linear equations (solvability, GEM and Cramer's rule)
4. Elementary functions I, construction and displacements of graphs (linear, quadratic, power function)
5. Elementary functions II, construction and displacements of graphs (rational fractional function, exponential and logarithmic function)
6. Elementary functions III, construction and displacements of graphs (trigonometric and cyclometric function)
7. Summary (linear algebra, basic properties of functions)
8. Polynomials (roots of a polynomial and their determination, Horner's scheme)
9. Limit and continuity of a function (proper and improper limit at a proper and improper point, basic properties and rules for calculation, continuity at a point and on an interval, properties and rules for calculating continuous functions)
10. Derivation 1st order (meaning, basic properties and rules, derivatives of elementary functions)
11. Summary (properties of functions, polynomials, limit and continuity of a function)
12. Differential (differential and its use)
13. Higher order derivatives (higher order derivatives, l'Hospital's rule)

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Sulkhan Mukhigulashvili, CSc.
RNDr. Zuzana Chvátalová, Ph.D.
Mgr. Martina Bobalová, Ph.D.
doc. András Rontó
doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

1.Basic concepts in mathematics
Matrixes (properties, matrix operations, calculating rank and inverse matrices)
Determinants (properties, rules and calculating determinants)
Systems of linear equations (solvability, GEM and Cramer's rule)
Elementary functions I, construction and displacements of graphs (linear, quadratic, power function)
Elementary functions II, construction and displacements of graphs (rational fractional function, exponential and logarithmic function)
Elementary functions III, construction and displacements of graphs (trigonometric and cyclometric function)
Review of the material covered
Polynomials (roots of a polynomial and their determination, Horner's scheme)
Limit and continuity of a function (proper and improper limit at a proper and improper point, basic properties and rules for calculation, continuity at a point and on an interval, properties and rules for calculating with continuous functions)
1st-order derivative (meaning, basic properties and rules, derivatives elementary functions)
Review of the material covered
Differential (differential and its use)

Elearning

eLearning: currently opened course