# 714-0365/02 – 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
LoginNameTuitorTeacher giving lectures
DOS14 Mgr. Marie Dostálová
KOT31 RNDr. Jan Kotůlek, Ph.D.
NIK01 Ing. Marek Nikodým, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
VRB30 RNDr. Helena Vrbenská
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Graded 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

### Recommended literature:

http://education-portal.com/academy/course/precalculus-course.html

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Program seminářů + individuální práce studentů ============================================== I. Základy matematické logiky: konstanta, proměnná, výrok, operace s výroky. Teorie množin: druhy množin, operace s množinami, číselné množiny, intervaly. Úpravy algebraických výrazů: mnohočleny, zlomky, mocniny, odmocniny. Úpravy algebraických výrazů: mnohočleny, zlomky, mocniny, odmocniny. Rovnice: lineární, lineární s parametrem, kvadratické (i v oboru komplexních čísel), iracionální, soustavy dvou lineárních rovnic o dvou neznámých Nerovnice: lineární, v součinovém a podílovém tvaru (řešení pomocí nulových bodů), kvadratické, soustavy. Absolutní hodnota. Geometrický význam absolutní hodnoty. Rovnice a nerovnice s absolutní hodnotou ( řešení pomocí nulových bodů). II. Funkce: vlastnosti, definiční obor, funkce lineární, kvadratická, kubická , iracionální, lomená. Exponenciální a logaritmické funkce. Pravidla pro logaritmování, logaritmování a odlogaritmování výrazů. Exponenciální rovnice a nerovnice. Goniometrické funkce, jejich grafy a hodnoty. Goniometrické rovnice a nerovnice. III. Analytická geometrie v rovině: vektory, přímka - typy rovnic, graf. Kružnice - typy rovnic, určení středu a poloměru doplněním na čtverec. Elipsa, hyperbola (graf lineární lomené funkce), parabola (graf kvadratické funkce). Určení základních parametrů doplněním na čtverec. IV. Posloupnosti a řady. Komplexní čísla. Individuální práce studentů =========================== 1 semestrální úloha - úpravy algebraických výrazů (3 h ) 1 semestrální úloha - řešení rovnic a nerovnic(3 h ) 1 semestrální úloha - elementární funkce a jejich grafy (3 h)

### Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Graded exercises evaluation Graded credit 100 (100) 0
Úloha Other task type 100  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
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