# 714-0366/02 – Mathematics I (MI)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor RNDr. Jan Kotůlek, Ph.D. Subject version guarantor Mgr. Monika Jahodová, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2000/2001 Year of cancellation 2019/2020 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
JAH0037 Mgr. Monika Jahodová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
ZID76 Mgr. Arnošt Žídek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 12+4

### Subject aims expressed by acquired skills and competences

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.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

The subject is divided into four chapters. In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications. In the third chapter we study linear algebra. We introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.

### Compulsory literature:

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003. [2] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 [3] NEUSTUPA, J.: Mathematics I., ČVUT, Praha 2004

### Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington 1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

### Way of continuous check of knowledge in the course of semester

Podmínky pro udělení zápočtu: Za účast na výuce student získá 10 bodů, v případě neúčasti může student získat body za zpracování zadaného programu. Za absolvování zápočtového testu z derivací může student získat maximálně 10 bodů, pro udělení zápočtu je nutné získat ze zápočtového testu alespoň 5 bodů. zkouška Kombinovanou zkoušku tvoří praktická část (60 minut, příklady) a teoretická část (20 minut, teoretické otázky). Praktická část je hodnocena 0 - 60 body, teoretická část 0 - 20 body. Aby student u zkoušky uspěl musí získat v praktické části nejméně 25 bodů a v teoretické části nejméně 5 bodů. klasifikace získané body známka 86 - 100 výborně 66 - 85 velmi dobře 51 - 65 dobře 0 - 50 nevyhověl Otázky k teoretické části zkoušky z předmětu Matematika I Lineární algebra 1. Determinant a jeho výpočet 2. Sarrusovo pravidlo 3. Výpočet determinantu řádu n>3 4. Definice matice, základní typy matic 5. Početní operace s maticemi 6. Inverzní matice a její určení 7. Hodnost matice 8. Soustavy lineárních algebraických rovnic 9. Frobeniova věta 10. Cramerovo pravidlo 11. Gaussova eliminační metoda 12. Analytická geometrie v prostoru 13. Geometrické vektory 14. Skalární součin vektorů a jeho význam 15. Vektorový součin vektorů a jeho význam 16. Smíšený součin vektorů a jeho význam 17. Rovnice roviny (vektorová, parametrické, obecná) 18. Rovnice přímky (vektorová, parametrické, obecná) Funkce jedné proměnné 1. Definice funkce jedné proměnné 2. Definiční obor funkce 3. Charakteristiky funkcí jedné proměnné 4. Funkce monotonní 5. Funkce sudá, lichá, periodická 6. Funkce prostá 7. Funkce inverzní 8.Funkce racionální lomená 9.Funkce exponenciální 10.Funkce logaritmická 11.Funkce goniometrické 12.Funkce cyklometrické 13.Geometrický a fyzikální význam derivace 14.Derivace součtu, součinu a podílu funkcí 15.Derivace složené funkce 16.Užití derivace 17.Extrémy funkce 18.Funkce konvexní, konkávní, inflexní body 19.Průběh funkce 20.Parametricky zadaná funkce

### E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz/M http://mdg.vsb.cz/wiki

### Other requirements

There are no other requierements

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-0365 ZM Basics of Mathematics Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

I. Functions of one real variable Definitions and basic properties, elementary functions, limit of the function, continuity of the functions, basic rules II. Differential calculus functions of one real variable The derivative of function (basic rules for differentiation), derivatives of selected functions, differential of the function, parametric differentiation, highes-order derivative, applications of the derivatives, monotonic functions and extremes of function, convexity and concavity of a function I. Linear algebra and analytical geometry Matrice (basic properties), determinants (basic properties, calculation, evaluation), matrix inversion, systems of linear equations, Cramer’s rule, Gaussian elimination, product of vectors (basic properties), analytical geometry in E3

### Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester, validity until: 2009/2010 Winter semester)
Task nameType of taskMax. number of points
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20 (20) 0
Written exam Written test 20  0
Examination Examination 80 (80) 0
Written examination Written examination 60  0
Oral Oral examination 20  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2017/2018 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2016/2017 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2015/2016 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2011/2012 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2010/2011 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2010/2011 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2009/2010 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2009/2010 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2009/2010 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Třinec 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Ostrava 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Šumperk 1 Compulsory study plan
2008/2009 (B2341) Engineering K Czech Uherský Brod 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Šumperk 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Uherský Brod 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Třinec 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Šumperk 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Uherský Brod 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Třinec 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Šumperk 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Uherský Brod 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Třinec 1 Compulsory study plan
2004/2005 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan
2001/2002 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering K Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner