# 230-0404/01 – Mathematics I (MI)

 Gurantor department Department of Mathematics Credits 5 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 summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
CER365 doc. Ing. Martin Čermák, Ph.D.
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
POS220 Ing. Lukáš Pospíšil, Ph.D.
STA50 RNDr. Jana Staňková, Ph.D.
URB0186 RNDr. Zbyněk Urban, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+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 toanalyze 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

Lectures
Individual consultations
Tutorials

### Summary

The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three basic parts of mathematics, according to which the learning material is structured. In Differential Calculus, the main motive is the preparation to general use of derivatives of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Analytic geometry, there are, based on vector calculus, described basic linear formations of three-dimensional Euclidean space and some tools to evaluate their mutual position from qualitative and also quantitative point of view.

### Compulsory literature:

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3. http://mdg.vsb.cz/portal/en/Mathematics1.pdf Bartsch, Hans Jochen: Handbook of Mathematical Formulas. Burdette, A.C.:An Introduction to Analytic Geometry and Calculus,Academic Press,1973.

### Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1. Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1. Jain, P.K.:A Textbook of Analytical Geometry of Three Dimensions,New Age International Publisher,1996. Moore,C: Math quations and inequalities, Science & Nature, 2014.

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

Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course, passing of written tests. The student will get 5 b for fulfilling the conditions. The student can get 0 - 15 b for the tests. (The student who gets the credit will be evaluated 5 - 20 b). The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.

### E-learning

http://www.studopory.vsb.cz http://mdg.vsb.cz/portal

### Other requirements

other requirements are not

### Prerequisities

Subject codeAbbreviationTitleRequirement
230-0400 ZM Basics of Mathematics Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Real function of one real variable. Operations with functions. (Basic) elementary functions. 2. Properties of functions - intersections with axes, sign of function, boundary, monotonicity, extremes, convexity, concavity, parity, simplicity, invertibility, periodicity. 3. Limit of a function, limit theorems, asmyptotes to a function graph. 4. Continuity and discontinuity of function. 5. Derivative of function - geometric and physical meaning. Derivative of basic elementary functions. Differentiation rules. Derivatives of higher orders. 6. Use of derivatives - L'Hospital rule, basic theorems of differential calculus, analysis of the course of a function. 7. Function differential, Taylor polynomial. 8. Arithmetic vector space. Linear independence vectors. 9. Matrices - types, special matrices, operations. 10. Determinant. Inverse matrix. Rank. 11. Systems of linear equations. Frobenius theorem. Gaussian elimination method. Cramer rule. 12. Line and plane in Euclidean space. Scalar, vector and mixed product of vectors. 13. Line and plane equations in E3 and their relative positions. 14. Distances and deviations of basic objects in E3.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30
Písemná zkouška Written test 60  25
Ústní zkouška Oral examination 20  5
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).

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (B1088A330001) Geoscience and Industrial Tourism P Czech Ostrava 2 Optional study plan
2021/2022 (B0724A290003) Mineral Economics P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0724A290004) Petroleum Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0724A290001) Mining of Mineral Resources P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0532A330034) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0724A290006) Process Engineering in Raw Materials P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0724A290007) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0532A330033) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0719A290001) Water – Strategic Resource P Czech Ostrava 1 Compulsory study plan
2021/2022 (B0712A290001) Waste Management and Mineral Processing P Czech Ostrava 1 Compulsory study plan
2021/2022 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2021/2022 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2021/2022 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2021/2022 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2020/2021 (B2110) Geological Engineering (2101R003) Geological Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0724A290003) Mineral Economics P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0724A290001) Mining of Mineral Resources P Czech Ostrava 1 Compulsory study plan
2020/2021 (B2102) Mineral Raw Materials (2102R006) Water Technologies and Water Management P Czech Ostrava 1 Compulsory study plan
2020/2021 (B3646) Geodesy and Cartography (3646R007) Engineering Geodesy P Czech Ostrava 1 Compulsory study plan
2020/2021 (B2102) Mineral Raw Materials (2102R001) Economics and Management in the Field of Raw Materials P Czech Ostrava 1 Compulsory study plan
2020/2021 (B2102) Mineral Raw Materials (3904R005) Environmental Engineering P Czech Ostrava 1 Compulsory study plan
2020/2021 (B1088A330001) Geoscience and Industrial Tourism P Czech Ostrava 2 Optional study plan
2020/2021 (B1316) Geodesy, Cartography and Geoinformatics (3646R006) Geoinformatics P Czech Ostrava 1 Compulsory study plan
2020/2021 (B3646) Geodesy and Cartography (3646R001) Mining Surveying P Czech Ostrava 1 Compulsory study plan
2020/2021 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism P Czech Ostrava 2 Optional study plan
2020/2021 (B2110) Geological Engineering (2101R004) Geoscience and Industrial Tourism P Czech Most 2 Optional study plan
2020/2021 (B0712A290001) Waste Management and Mineral Processing P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0724A290006) Process Engineering in Raw Materials P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0719A290001) Water – Strategic Resource P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0724A290004) Petroleum Engineering P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0724A290001) Mining of Mineral Resources P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0712A290001) Waste Management and Mineral Processing P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner