# 714-0016/01 – Mathematics (M)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor Mgr. Jakub Stryja, Ph.D. Subject version guarantor Mgr. Jakub Stryja, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2014/2015 Year of cancellation 2019/2020 Intended for the faculties FBI Intended for study types Follow-up Master
Instruction secured by
STR78 Mgr. Jakub Stryja, 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

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 and verify each step of an algorithm, generalize achieved results, analyze correctness of results with respect to given conditions, apply these methods while solving technical problems.

### Teaching methods

Lectures
Individual consultations
Tutorials
Project work

### Summary

Double and triple integrals and their applications. Line integral and its applications. Infinite series, power series.

### Compulsory literature:

Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1

### Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

### Other requirements

No more requirements are put on the student.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1 Integral calculus of functions of several independent variables. Two-dimensional integrals on coordinate rectangle, on bounded subset of R2. 2 Transformation two-dimensional integrals. 3 Geometrical and physical applications. 4 Three-dimensional integrals on coordinate cube, on bounded subset of R3. transformation of three-dimensional integrals. 5 Geometrical and physical applications. 6 Line integral of the first and of the second kind. 7 Independence line integral on path, Green´s theorem. 8 Applications. 9 Series. Infinite number series. Definition, sum of a series, necessary convergence condition, harmonic series, geometric series. 10 Convergency tests, ratio test, Cauchy's root test, comparison test, integral test. 11 Alternating series - absolute and conditional convergency, Lebniz test. 12 Power series - convergency interval, radius of convergence, sum of a powerseries. 13 Taylor expansion, applications. 14 Reserve.

### Conditions for subject completion

Full-time form (validity from: 2014/2015 Winter semester, validity until: 2019/2020 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 20  10
Examination Examination 80 (80) 31
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2017/2018 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2014/2015 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

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