# 714-0365/01 – Basics of Mathematics (ZM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 2 Subject guarantor Mgr. Milena Luňáčková, Ph.D. Subject version guarantor RNDr. Helena Vrbenská Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 1999/2000 Year of cancellation 2007/2008 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DOL10 RNDr. Milan Doležal, CSc.
DOS14 Mgr. Marie Dostálová
DUD88 Mgr. Krista Dudková
HOM44 PaedDr. Zdenka Homolová
KOT31 RNDr. Jan Kotůlek, Ph.D.
LUN44 Mgr. Milena Luňáčková, Ph.D.
NIK01 Ing. Marek Nikodým, Ph.D.
OTI73 Mgr. Petr Otipka
SKA74 Mgr. Sylvie Skalníková
TUM20 RNDr. Milan Tůma
VRB30 RNDr. Helena Vrbenská
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 0+2
Part-time Credit 0+8

### 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.

Seminars
Other activities

### Summary

The set of real numbers, operations with algebraic expressions, equations and inequalities, functions, exponential and logarithmic equations, trigonometric functions and equations, analytic geometry, arithmetic and geometric sequences.

### Compulsory literature:

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003. [2] https://www.khanacademy.org/math/ Harshbarger, R.J. - Teynolds, J.J.: Calculus with Applications. D.C. Heath and Company, Lexington 1990, ISBN 0-669-21145-1

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Týden Náplň cvičení a seminářů -------------------------------------------------------------------------------- 1 Základy matematické logiky: konstanta, proměnná, výrok, operace s výroky. Teorie množin: druhy množin, operace s množinami, číselné množiny, intervaly. 2 Úpravy algebraických výrazů: mnohočleny, zlomky, mocniny, odmocniny. 3 Úpravy algebraických výrazů: mnohočleny, zlomky, mocniny, odmocniny. 4 Rovnice: lineární, lineární s parametrem, kvadratické (i v oboru komplexních čísel), iracionální, soustavy dvou lineárních rovnic o dvou neznámých 5 Nerovnice: lineární, v součinovém a podílovém tvaru (řešení pomocí nulových bodů), kvadratické, soustavy. 6 Absolutní hodnota. Geometrický význam absolutní hodnoty. Rovnice a nerovnice s absolutní hodnotou ( řešení pomocí nulových bodů). 7 Funkce: vlastnosti, definiční obor, funkce lineární, kvadratická, kubická , iracionální, lomená. 8 Exponenciální a logaritmické funkce. Pravidla pro logaritmování, logaritmování a odlogaritmování výrazů. Exponenciální rovnice a nerovnice. 9 Goniometrické funkce, jejich grafy a hodnoty. Goniometrické rovnice a nerovnice. 10 Analytická geometrie v rovině: vektory, přímka - typy rovnic, graf, kružnice - typy rovnic, určení středu a poloměru doplněním na čtverec. 11 Elipsa, hyperbola (graf lineární lomené funkce), parabola (graf kvadratické funkce). Určení základních parametrů doplněním na čtverec. 12 Posloupnosti a řady. 13 Komplexní čísla. 14 Závěrečný test.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
Min. number of points
Exercises evaluation Credit 85 (85) 0
Written exam Written test 60  0
Other task type Other task type 25  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2007/2008 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (60) P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (70) P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2341) Engineering (3708R028) Transport Technology (50) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2006/2007 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (50) P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Šumperk 1 Compulsory study plan
2005/2006 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 1 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 1 Compulsory study plan
2001/2002 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner