# 714-0211/01 – Mathematics IV (MgrM4)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor Mgr. Jiří Krček Subject version guarantor Mgr. Jiří Krček Study level undergraduate or graduate Requirement Compulsory Year 1 Semester winter Study language Czech Year of introduction 2015/2016 Year of cancellation 2019/2020 Intended for the faculties FAST Intended for study types Follow-up Master
Instruction secured by
KRC76 Mgr. Jiří Krček
KRE40 doc. RNDr. Pavel Kreml, CSc.
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

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

Passing the course, requirements Course-credit -participation on tutorials is obligatory, 20% of absence can be apologized, -elaborate programs, -pass the written tests, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points.

### 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. 14. Reserve.

### Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester, validity until: 2019/2020 Summer semester)
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:

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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 (3607T036) Transport Constructions (01) Transport Constructions P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T036) Transport Constructions (02) Traffic Engineering P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T049) Realization of Constructions P Czech Ostrava 1 Compulsory study plan
2017/2018 (N3607) Civil Engineering (3607T021) Building Materials and Diagnostics of Structures P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T036) Transport Constructions (01) Transport Constructions P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T036) Transport Constructions (02) Traffic Engineering P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T049) Realization of Constructions P Czech Ostrava 1 Compulsory study plan
2016/2017 (N3607) Civil Engineering (3607T021) Building Materials and Diagnostics of Structures P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3607) Civil Engineering (3607T049) Realization of Constructions P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3607) Civil Engineering (3607T021) Building Materials and Diagnostics of Structures P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3607) Civil Engineering (3607T036) Transport Constructions (01) Transport Constructions P Czech Ostrava 1 Compulsory study plan
2015/2016 (N3607) Civil Engineering (3607T036) Transport Constructions (02) Traffic Engineering P Czech Ostrava 1 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner