# 230-0400/03 – Basics of Mathematics (ZM)

 Gurantor department Department of Mathematics Credits 2 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 Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
JAR71 Mgr. Marcela Jarošová
Extent of instruction for forms of study
Form of studyWay of compl.Extent

### 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:

Lang, S.: Basic Mathematics, Springer-Verlag New York Inc. 1998, ISBN: 9780387967875. Harshbarger, R.J., Teynolds, J.J.: Calculus with Applications. D.C. Heath and Company, Lexington 1990, ISBN 0-669-21145-1. http://www.studopory.vsb.cz/studijnimaterialy/Zaklady_matematiky/zm.pdf

### Recommended literature:

http://mdg.vsb.cz/portal/ Bartsch, Hans Jochen: Handbook of Mathematical Formulas. Moore,C: Math quations and inequalities, Science & Nature, 2014. Burdette, A.C.:An Introduction to Analytic Geometry and Calculus,Academic Press,1973.

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

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.

### Other requirements

There are no other requests.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

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

Part-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Written test Written test 100  51
Mandatory attendence parzicipation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

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2020/2021 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 1 Compulsory study plan
2020/2021 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 1 Compulsory study plan
2020/2021 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
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2020/2021 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 1 Compulsory study plan
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2020/2021 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0712A290001) Waste Management and Mineral Processing K Czech Most 1 Compulsory study plan
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2019/2020 (B2111) Mining (2101R014) Blasting Operations in Mining Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2111) Mining (2101R013) Mining of Mineral Resources and Their Utilization K Czech Most 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials K Czech Most 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management K Czech Most 1 Compulsory study plan
2019/2020 (B3646) Geodesy and Cartography (3646R001) Mining Surveying K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy K Czech Most 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (2102R013) Processing of Raw Materials and Recycling K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Ostrava 1 Compulsory study plan
2019/2020 (B2102) Mineral Raw Materials (3904R022) Waste Treatment and Disposal K Czech Most 1 Compulsory study plan
2019/2020 (B0724A290001) Mining of Mineral Resources K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0724A290001) Mining of Mineral Resources K Czech Most 1 Compulsory study plan
2019/2020 (B0712A290001) Waste Management and Mineral Processing K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0712A290001) Waste Management and Mineral Processing K Czech Most 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner