714-0211/04 – Mathematics IV (MgrM4)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorMgr. Jiří KrčekSubject version guarantorMgr. Jiří Krček
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageEnglish
Year of introduction2015/2016Year of cancellation2019/2020
Intended for the facultiesFASTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
KRE40 doc. RNDr. Pavel Kreml, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 16+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

Summary

Integral calculus of functions of several independent variables: double and triple integrals, vector analysis, line integral of the first and the second kind.

Compulsory literature:

http://www.studopory.vsb.cz http://www.studopory.vsb.cz/studijnimaterialy/MatematikaIII/Matematika3_obsah.pdf

Recommended literature:

http://homen.vsb.cz/~kre40/matematika.html#m3 Burda, P. - Doležalová, J.: Integrální počet funkcí více proměnných – Matematika IIIb. Skriptum VŠB, Ostrava 2003. ISBN 80-248-0454-9. Burda, P. - Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB, Ostrava 2002. ISBN 80-248-0028-4. Trench, W: Introduction to Real Analysis. http://ramanujan.math.trinity.edu/wtrench/texts/index.shtml (free download)

Way of continuous check of knowledge in the course of semester

E-learning

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. Double integral over a rectangular domain and over a general regular domain. 2. Transformation to polar and generalized polar coordinates. 3. Applications of double integrals. 4. Triple integral over a rectangular hexahedron and over a general regular domain. 5. Transformation to cylindrical and generalized cylindrical coordinates. 6. Transformation to spherical and generalized spherical coordinates. 7. Applications of triple integrals. 8. Vector fields. Divergence and rotation of vector fields. Line integrals. 9. Line integral of a scalar field. 10. Line integral of a vector field. 11. Green’s theorem and the path independence. 12. Applications of line integrals. 13. Applications in the civil engineering.

Conditions for subject completion

Part-time form (validity from: 2015/2016 Winter semester, validity until: 2019/2020 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80 (80) 31 3
                Písemná zkouška Written examination 60  25
                Ústní zkouška Oral examination 20  5
Mandatory attendence participation:

Show history

Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2017/2018 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction K English Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T021) Building Materials and Diagnostics of Structures K English Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T036) Transport Constructions (01) Transport Constructions K English Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T036) Transport Constructions (02) Traffic Engineering K English Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T035) Geotechnics K English Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction K English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

Předmět neobsahuje žádné hodnocení.