714-0015/01 – Engineering Mathematics (IM)

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 introduction2006/2007Year 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
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

Podmínky absolvování předmětu Podmínky pro udělení zápočtu (prezenční studium): - účast ve cvičení, 20 % neúčasti lze omluvit, - odevzdání programů zadaných vedoucím cvičení v předepsané úpravě, - absolvování písemných testů, každý test je možno jednou opravit, nutno získat minimálně 5 bodů. Za splnění podmínek získá student 5 bodů. Za testy může získat student 5 - 15 bodů. (Student, který získá zápočet, bude hodnocen 10 - 20 bodů). Podmínky pro udělení zápočtu (kombinované studium): Za účast na konzultacích může student získat 5 - 20 bodů, v případě neúčasti může student získat 5 bodů za zpracování zadaného programu. Požadavky ke zkoušce: Podmínkou pro účast na zkoušce je zapsaný zápočet z příslušného předmětu. Písemná část zkoušky bude hodnocena 0 - 60 body, za její úspěšné absolvování bude považován zisk 25 bodů. Ústní část zkoušky bude hodnocena 0 - 20 body, za její úspěšné absolvování bude považován zisk 5 bodů. Po sečtení bodů získaných za zápočet, písemnou a ústní část zkoušky bude student hodnocen výborně, velmi dobře, dobře a nevyhověl, podle tabulky studijního a zkušebního řádu VŠB - TUO. Pro zapsání zkoušky podle tabulky musí student úspěšně absolvovat obě části kombinované zkoušky a dosáhnout potřebného počtu bodů. Bodové hodnocení: 86 - 100 výborně 66 - 85 velmi dobře 51 - 65 dobře 0 - 50 nevyhověl Otázky ke zkoušce: 1. Dvojný integrál a jeho aplikace 2. Transformace dvojného intergrálu 3. Trojný integrál a jeho aplikace 4. Křivky v E3 a jejich parametrizace. 5. Křivkový integrál I. druhu: definice, vlastnosti, výpočet, užití.. 6. Křivkový integrál II. druhu: definice, vlastnosti, výpočet, užití. 7. Greenova věta - formulace, důkaz, užití (obsah rovinného oboru). 8. Nezávislost křivkového integrálu II. druhu na int. cestě, potenciálové pole. 9. Řady s kladnými členy, kriteria konvergence. 10. Alternující řady. 11. Mocninné řady - obor konvergence 12. Součet mocninné řady. 13. Taylorův rozvoj 14. Aplikace mocninných řad

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

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
2018/2019 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2018/2019 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2018/2019 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2018/2019 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2014/2015 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2014/2015 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2014/2015 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3908) Fire Protection and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3908) Fire Protection and Industrial Safety (3908T005) Engineering Safety of Persons and Property P Czech Ostrava 1 Compulsory study plan
2009/2010 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2009/2010 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2009/2010 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3908) Fire Protection and Industrial Safety (3908T007) Safety and Security Planning P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety (30) Fire Protection Engineering and Industrial Safety P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety (30) Fire Protection Engineering and Industrial Safety P 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 - FBI - P 2014/2015 Full-time Czech Optional FBI - Faculty of Safety Engineering stu. block