# 714-0565/01 – Basics of Mathematics (ZM)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 1 Subject guarantor Mgr. Dagmar Dlouhá, Ph.D. Subject version guarantor doc. RNDr. Radim Havelek, Ph.D. Study level undergraduate or graduate Study language Czech Year of introduction 1999/2000 Year of cancellation 2010/2011 Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
BUR30 doc. RNDr. Pavel Burda, CSc.
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
FUN01 Mgr. Taťána Funioková, Ph.D.
HAV10 doc. RNDr. Radim Havelek, Ph.D.
JED20 Mgr. Lumír Jedelský
KOL70 doc. Dr. Mgr. Ivan Kolomazník
RES50 RNDr. Čestmír Restl
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time 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 ================= Exercises --------- Conditions for obtaining credit points (CP): - participation in exercises, 20% can be to apologize - completion of two programs, both 0-20 CP - completion of two written tests, both 0-30 CP The requirements are analogous to the program of the lectures.

### 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: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation Credit 85 (85) 0
Written exam Written test 60  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2010/2011 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2009/2010 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3904R028) Environmental Biotechnology P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3902R033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2111) Mining (2101R008) Mining Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2008/2009 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Ostrava 1 Optional study plan
2008/2009 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (10) Geoscience and Industrial Tourism P Czech Most 1 Optional study plan
2008/2009 (B2102) Mineral Raw Materials (6209R013) Information and System Management P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3904R028) Environmental Biotechnology P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Compulsory study plan
2007/2008 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3902R033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2111) Mining (2101R008) Mining Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management P Czech Ostrava 1 Compulsory study plan
2007/2008 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2007/2008 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Ostrava 1 Optional study plan
2007/2008 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (10) Geoscience and Industrial Tourism P Czech Most 1 Optional study plan
2007/2008 (B2102) Mineral Raw Materials (6209R013) Information and System Management P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Ostrava 1 Optional study plan
2006/2007 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (6209R013) Information and System Management P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (3904R028) Environmental Biotechnology P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2110) Geological Engineering (2101T003) Geological Engineering (00) Geologické inženýrství P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2102) Mineral Raw Materials (3902R033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B2111) Mining (2101R008) Mining Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (10) Geoscience and Industrial Tourism P Czech Most 1 Optional study plan
2006/2007 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2006/2007 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2111) Mining (2101R008) Mining Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3902R033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Optional study plan
2005/2006 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Ostrava 1 Optional study plan
2005/2006 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Most 1 Optional study plan
2005/2006 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (10) Geoscience and Industrial Tourism P Czech Ostrava 1 Optional study plan
2005/2006 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (10) Geoscience and Industrial Tourism P Czech Most 1 Optional study plan
2005/2006 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (6209R013) Information and System Management P Czech Ostrava 1 Optional study plan
2005/2006 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2005/2006 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3902R006) Automation and Computers in Raw Material Industry P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2111) Mining (2101R008) Mining Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3902R033) System Engineering in Raw Materials Industry P Czech Ostrava 1 Optional study plan
2004/2005 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Ostrava 1 Optional study plan
2004/2005 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (10) Geoscience and Industrial Tourism P Czech Ostrava 1 Optional study plan
2004/2005 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (6209R013) Information and System Management P Czech Ostrava 1 Optional study plan
2004/2005 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2004/2005 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (3911R001) Applied Physics of Materials P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling P Czech Ostrava 1 Compulsory study plan
2004/2005 (B2102) Mineral Raw Materials (2102R003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2102) Mineral Raw Materials (2102R012) Management of Resources of Building Mineral Raw Materials P Czech Ostrava 1 Choice-compulsory study plan
2003/2004 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism (00) GMT P Czech Ostrava 1 Optional study plan
2002/2003 (B3908) Fire Protection and Industrial Safety (3908R003) Emergency Planning and Crisis Management P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner