310-2111/02 – Mathematics I (MI)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorRNDr. Jan Kotůlek, Ph.D.Subject version guarantorRNDr. Jan Kotůlek, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation2022/2023
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAR024 Ing. Petr Harasim, Ph.D.
JAH0037 Mgr. Monika Jahodová, Ph.D.
KOT31 RNDr. Jan Kotůlek, Ph.D.
MOR74 Mgr. Zuzana Morávková, Ph.D.
MUL0086 RNDr. PhDr. Ivo Müller, Ph.D.
OTI73 Mgr. Petr Otipka, Ph.D.
KAH14 Mgr. Marcela Rabasová, Ph.D.
RIE0053 Mgr. Tomáš Riemel
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 13+4

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

Lectures
Individual consultations
Tutorials
Other activities

Summary

The subject is divided into four chapters. In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications. In the third chapter we study linear algebra. We introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.

Compulsory literature:

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003. [2] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 [3] NEUSTUPA, J.: Mathematics I., ČVUT, Praha 2004

Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington 1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

Way of continuous check of knowledge in the course of semester

Written test and both practical and theoretical exam

E-learning

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

Other requirements

There are no other requierements

Prerequisities

Subject codeAbbreviationTitleRequirement
310-2110 ZM Basics of Mathematics Compulsory

Co-requisities

Subject codeAbbreviationTitle
310-2110 ZM Basics of Mathematics

Subject syllabus:

I. Functions of one real variable Definitions and basic properties, elementary functions, limit of the function, continuity of the functions, basic rules II. Differential calculus functions of one real variable The derivative of function (basic rules for differentiation), derivatives of selected functions, differential of the function, parametric differentiation, highes-order derivative, applications of the derivatives, monotonic functions and extremes of function, convexity and concavity of a function III. Linear algebra and analytical geometry Matrices (basic properties), determinants (basic properties, calculation, evaluation), matrix inversion, systems of linear equations, Cramer’s rule, Gaussian elimination, product of vectors (basic properties), analytical geometry in E3

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2020/2021 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2020/2021 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2020/2021 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan
2020/2021 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3907) Energetics (3907R012) Energetics of the 21st Century K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Šumperk 1 Compulsory study plan
2019/2020 (B0715A270011) Engineering K Czech Uherský Brod 1 Compulsory study plan
2019/2020 (B0713A070002) Energetics and Environments K Czech Ostrava 1 Compulsory study plan
2019/2020 (B0715A040001) Transport Systems and Equipment K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
Subject block without study plan - FS - K - cs 2021/2022 Part-time Czech Optional FS - Faculty of Mechanical Engineering stu. block

Assessment of instruction



2020/2021 Winter
2019/2020 Winter