Course detail

Mathematics 1

FP-ma1PAcad. year: 2022/2023

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. RNDr. Bedřich Půža, CSc.

Department

Institute of Informatics (ÚI)

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.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Instructing is divided into lectures and exercises. Lectures are focused on the theory referring to applications, exercises on practical calculations and solving of application tasks.

Assesment methods and criteria linked to learning outcomes

Credit requirements:

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

Exam requirements:

The exam has a written and an oral part, with the focus of the exam being the oral part.

For all tasks in the written part, the calculation must be written down, 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 graded "F" (unsatisfactory) and the student does not proceed to the oral part.
If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.


Completion of the subject for students with individual study:
Passing the comprehensive control test and achieving at least 55% points.
Awarding credit is a necessary condition for taking the exam.
The exam has a written and an oral part, with the focus of the exam being the oral part.
For all tasks in the written part, the calculation must be written down, 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 graded "F" (unsatisfactory) and the student does not proceed to the oral part.
If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory) and the student does not proceed to the oral part.
The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.

Course curriculum

1. Basic mathematical concepts, numbers (basics of set theory - sets, operations with them, Vennov diagrams, real and
complex numbers - properties, counting, absolute value, intervals, complex numbers plane)
2. Matrices and determinants (matrices and operations with them, properties and calculation of determinants)
3. Systems of linear equations (solving conditions, Gaussian elimination method, Cramer rule)
4. Function (real function of one real variable and its basic characteristics - odd, even, periodic, limited and
monotone functions and its graph, elementary functions -power, goniometric and cyclometric functions, exponential and
logarithmic functions, general power)
5. Operations with functions (rational functions with functions, compound, simple, inverse functions, elementary structures and
graph shifts)
6. Polynomials and rational fracture functions (zero points - polynomial roots, polynomial decomposition, Horner scheme, pure
and neryze-laced rational function, decomposition into partial fractions)
7. Limit (own and improper limit at own and stepped points, basic properties, limit of elementary functions,
rules for calculating the limit)
8. Continuity (continuity at point and interval, continuity of elementary functions, rules for counting with continuous functions,
properties of functions continuous at a closed interval)
9. Sequences (Real Number Sequences, Restricted and Monotone Sequences, Sequence Limit)
10. Derivatives of the 1st order (sense, basic properties and rules, derivation of elementary functions)
11. Derivatives of the first and higher order (differential and its use, higher order derivation, l'Hospitality rule)
12. The course of function I (monotony, local and absolute extremes of function)
13. Functional function II (convexity and concavity, function asymptotes, complete description of function behavior)

Work placements

Not applicable.

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).

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

Participation in exercises is controlled.

Recommended optional programme components

Not applicable.

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 Bachelor's

    branch BAK-UAD-D , 1 year of study, winter semester, compulsory
    branch BAK-EP , 1 year of study, winter semester, compulsory

  • Programme BAK-EP 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

doc. Mgr. Veronika Novotná, Ph.D.
doc. András Rontó
doc. RNDr. Sulkhan Mukhigulashvili, CSc.
doc. RNDr. Bedřich Půža, CSc.

Syllabus

1. Basic mathematical concepts
2. Matrices (properties, matrix operations, rank calculation and inverse matrices)
3. Determinants (properties, rules and calculation of determinants)
4. Systems of linear equations (solvability, GEM and Cramer's rule)
5. Functions of one variable (basic characteristics of functions, properties, rational operations with functions, composite, simple, inverse functions)
6. Polynomials (roots of a polynomial and their determination, Horner's scheme)
7. Summary (linear algebra, basic properties of functions)
8. Elementary functions (properties, constructions and displacements of graphs)
9. Limit and continuity (eigen and non-eigen limits at an eigen and non-eigen point, basic properties and rules for calculation, continuity at a point and on an interval, properties and rules for calculating with continuous functions)
10. Sequences (bounded and monotonic sequences of real numbers, sequence limit)
11. Derivation of the 1st order (meaning, basic properties and rules, derivation of elementary functions)
12. Summary (properties of functions, polynomials, limits and continuity of functions)
13. Differential and derivatives of higher orders (differential and its use, derivatives of higher orders, l'Hospital's rule)

Exercise

26 hod., compulsory

Teacher / Lecturer

RNDr. Zuzana Chvátalová, Ph.D.
doc. RNDr. Sulkhan Mukhigulashvili, CSc.

Syllabus

1. Basic mathematical concepts I
2. Basic mathematical concepts II
3. Matrices (properties, matrix operations, rank calculation and inverse matrices)
4. Determinants (properties, rules and calculation of determinants)
5. Systems of linear equations (solvability, GEM and Cramer's rule)
6. Functions of one variable (basic characteristics of functions, properties, rational operations with functions, compound, simple, inverse function)
7. Repetition (linear algebra, basic properties of functions)
8. Polynomials (roots of a polynomial and their determination, Horner's scheme)
9. Elementary functions (properties, constructions and displacements of graphs)
10. Limit and continuity (eigen and non-eigen limits at an eigen and non-eigen point, basic properties and rules for calculation, continuity at a point and on an interval, properties and rules for calculating with continuous functions)
11. Sequences (bounded and monotonic sequences of real numbers, sequence limit)
12. Derivation of the 1st order (meaning, basic properties and rules, derivation of elementary functions)
13. Derivation of the 1st order of elementary functions

Elearning

eLearning: currently opened course