# 714-0565/07 – Basics of Mathematics (ZM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 1 Subject guarantor Mgr. Dagmar Dlouhá, Ph.D. Subject version guarantor Mgr. Dagmar Dlouhá, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language English Year of introduction 2016/2017 Year of cancellation Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DRO03 Mgr. Jaroslav Drobek, Ph.D.
JED20 Mgr. Lumír Jedelský
KOT31 RNDr. Jan Kotůlek, Ph.D.
POL12 RNDr. Jiří Poláček, CSc.
KAH14 Mgr. Marcela Rabasová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Graded credit 0+2

### 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

Individual consultations
Tutorials
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] Harshbarger, R.J. - Teynolds, J.J.: Calculus with Applications. D.C. Heath and Company, Lexington 1990, ISBN 0-669-21145-1

### Recommended literature:

Basic textbooks on mathematics. http://mdg.vsb.cz/M

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

Tests and credits ================= Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize, - successful passing of the test in secondary school mathematics, minimun 51 points, - student can ask for writing of the test during semester.

### Další požadavky na studenta

There are no other requests.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Week. Tutorial -------------- 1st Functions: properties, domain, linear, quadratic, cubic, irrational and rational functions. 2nd Exponential and logarithmic functions. Evaluation of logarithms. Exponential equations and inequalities. 3rd Goniometric functions, their graphs and values. Trigonometric equations and inequalities. 4th Mathematical logic: constants, variables, statements and operations. 5th Set theory: types of sets, operations with sets, sets of numbers, intervals. 6th Algebraic expressions: polynomials, fractions, powers, roots. 7th Equations: linear, linear with parameters, quadratic, irrational, systems of two linear equations. 8th Inequalities: linear, quadratic, systems. 9th Absolutní value: geometric interpretation, equations and inequalities. 10th Basics of analytical geometry: vectors, lines, circle, determination of the center and radius. 11th Elipsis, hyperbole, parabole: determination of parameters. 12th Sequences and series. 13th Complex numbers. 14th Tests and credits.

### Conditions for subject completion

Full-time form (validity from: 2016/2017 Winter semester)
Task nameType of taskMax. number of points
Min. number of points
Graded credit Graded credit 100 (100) 51
Test Written test 100  51
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (B2110) Geological Engineering (2101R003) Geological Engineering P English Ostrava 1 Compulsory study plan
2018/2019 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P English Ostrava 1 Compulsory study plan
2018/2019 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization P English Ostrava 1 Compulsory study plan
2017/2018 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P English Ostrava 1 Compulsory study plan
2017/2018 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization P English Ostrava 1 Compulsory study plan
2017/2018 (B2110) Geological Engineering (2101R003) Geological Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P English Ostrava 1 Compulsory study plan
2016/2017 (B2110) Geological Engineering (2101R003) Geological Engineering P English Ostrava 1 Compulsory study plan
2016/2017 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization P English Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner