Course detail

Mathematics 1

FP-Bma1PAcad. year: 2022/2023

Předmět je součástí teoretického základu oboru. MA1 slouží ke sjednocení a doplnění SŠ znalostí studentů v oblastech v další výuce nezbytných základních matematických pojmů, naučí studenty s porozuměním využívat aparátu lineární algebry k řešení soustav lineárních rovnic a diferenciálního počtu funkcí jedné proměnné ke studiu průběhu funkce jedné proměnné (včetně základních aplikací v ekonomických disciplínách).

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

Získané vědomosti a praktické matematické dovednosti zejména budou oporou pro získávání vědomostí a rozšiřování dovedností v oborech s ekonomickým zaměřením a pro korektní využívání matematických software a dále budou důležitým východiskem pro osvojování nových poznatků v navazujících předmětech matematického charakteru.

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

Základní matematické pojmy - množiny, čísla; matice, determinanty - soustavy lineárních rovnic a jejich řešení; diferenciální počet funkcí jedné reálné proměnné - základní charakteristiky, elementární funkce, polynomy a racionální lomené funkce, limita, spojitost, derivace - průběh funkce

Work placements

Not applicable.

Aims

Cílem je zvládnout řešení systémů lineárních rovnic a podrobnou analýzu dějů popsaných reálnou funkcí jedné reálné proměnné včetně realizace potřebných výpočtů obecně i v ekonomických aplikacích (i s ohledem na používání výpočetní techniky).

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

Attendance at exercises (seminars) is controlled.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Marošová, M., Mezník,I.: Cvičení z matematiky I. FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o.Brno, Brno 2008
Mezník,I.:Matematika I.FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o. Brno,Brno 2008

Recommended reading

Not applicable.

Elearning

eLearning: currently opened course

Classification of course in study plans

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

Type of course unit

 

Lecture

26 hod., compulsory

Teacher / Lecturer

Mgr. Martina Bobalová, Ph.D.

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

Mgr. Martina Bobalová, Ph.D.

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