# 230-0301/02 – Mathematics I (MI)

 Gurantor department Department of Mathematics Credits 6 Subject guarantor Mgr. Kateřina Kozlová, Ph.D. Subject version guarantor RNDr. Jana Volná, 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 FBI Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
CER365 doc. Ing. Martin Čermák, Ph.D.
PAL39 RNDr. Radomír Paláček, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 24+0

### 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 functions of one real variable, the derivation of a function of one variable. Derivations of higher orders. Investigating the behaviour of functions. Antiderivative and the indefinite integral, some properties, elementary methods of integration. Linear algebra: Arithmetic vectors, matrices, determinants, systems of linear algebraic equations.

### Compulsory literature:

[1] Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 [2] http://mdg.vsb.cz/portal/en/Mathematics1.pdf

### Recommended literature:

[1] Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 [2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 [3] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

### E-learning

http://mdg.vsb.cz/portal/en/Mathematics1.pdf

### Další požadavky na studenta

No more requirements are put on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Functions of one real variable Definitions and basic properties, elementary functions, limit of the function, continuity of the functions , basic rules. 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, higher-order derivative, applications of the derivatives, monotonic functions and extremes of function, convexity and concavity of a function. Linear algebra and analytical geometry Matrix (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 yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B3908) Fire Protection and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2019/2020 (B3908) Fire Protection and Industrial Safety K Czech Praha 1 Compulsory study plan
2019/2020 (B3908) Fire Protection and Industrial Safety K Czech Lázně Bohdaneč 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner