714-0016/01 – Mathematics (M)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorMgr. Jakub Stryja, Ph.D.Subject version guarantorMgr. Jakub Stryja, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2014/2015Year of cancellation
Intended for the facultiesFBIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
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

Way of continuous check of knowledge in the course of semester

E-learning

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:

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)
Task nameType of taskMax. number of points
(act. for subtasks)
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:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy 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

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner