# 714-0066/01 – Bachelor Mathematics I (BMI)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor doc. RNDr. Jarmila Doležalová, CSc. Subject version guarantor RNDr. Lubomír Pavelka, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2002/2003 Year of cancellation 2008/2009 Intended for the faculties FBI Intended for study types Bachelor
Instruction secured by
H1O40 Mgr. Iveta Cholevová, Ph.D.
DRO03 Mgr. Jaroslav Drobek, Ph.D.
KRA44 Mgr. Kateřina Kozlová, Ph.D.
PAV20 RNDr. Lubomír Pavelka, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
ZID76 Mgr. Arnošt Žídek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

This course is closed. Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics. This course is closed.

### Teaching methods

Individual consultations
Tutorials
Other activities

### Summary

The functions of one real variable, the derivation of a function of one variable. Derivations of higher orders. Investigating the behaviour of functions. Antiderivative and the indefinite integral, some properties, elementary methods of integration. Linear algebra: Arithmetic vectors, matrices, determinants, systems of linear algebraic equations.

### Compulsory literature:

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3

### Recommended literature:

[1] Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 [2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 [3] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Funkce jedné reálné proměnné Definiční obor, obor hodnot, funkce sudá, lichá, periodická, ohraničená, neohraničená, monotonní, složená, prostá, inverzní. Elementární funkce. Limita funkce, spojitost funkce. Derivace funkce jedné proměnné Definice, geometrický a fyzikální význam. Vzorce a pravidla pro derivování. Derivace vyšších řádů. Diferenciál funkce. L´Hospitalovo pravidlo monotonnost, lokální extrémy, konvexnost, konkávnost, inflexní body, asymptoty. Derivace parametricky zadané funkce. Lineární algebra Aritmetické vektory, operace, lineární závislost a nezávislost. Matice, hodnost matice, operace s maticemi. Typy matic - regulární, jednotková, inverzní. Determinanty, definice, vlastnosti, výpočet hodnoty. Soustavy lineárních algebraických rovnic, Cramerovo pravidlo, Frobeniova věta, Gaussova eliminační metoda. Analytická geometrie v prostoru Geometrické vektory, operace s nimi. Skalární, vektorový, smíšený součin a jejich užití. Analytické vyjádření roviny a přímky v prostoru, jejich vzájemné poloha, metrické úlohy.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Min. number of pointsMax. počet pokusů
Exercises evaluation and Examination Credit and Examination 100 (100) 51 3
Exercises evaluation Credit 20 (20) 0 3
Written exam Written test 15  0 3
Examination Examination 80 (80) 0 3
Written examination Written examination 60  0 3
Oral Oral examination 20  0 3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2008/2009 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava Compulsory study plan
2007/2008 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2006/2007 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2005/2006 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2004/2005 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan
2003/2004 (B3908) Fire Protection and Industrial Safety (3908R999) Společné studium FBI P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

### Assessment of instruction

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