230-0224/01 – Repetition of Mathematics 4 (Repet 4)

Gurantor departmentDepartment of MathematicsCredits1
Subject guarantorMgr. Jitka Krčková, Ph.D.Subject version guarantorMgr. Jitka Krčková, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageCzech
Year of introduction2018/2019Year of cancellation
Intended for the facultiesFASTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC23 Mgr. Jitka Krčková, Ph.D.
KRE40 doc. RNDr. Pavel Kreml, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 0+2
Combined Credit 0+16

Subject aims expressed by acquired skills and competences

Mathematics is an 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 analyse problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyse 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

Tutorials

Summary

Repetition of Mathematics 4 is intended for students who, for whatever reasons, fail the exam of Mathematics IV and are interested in passing this exam. Its content essentially coincides with the content of the course Mathematics IV. The aim is to enable better understanding of mathematics by the solving of concrete examples and problems. Repetition will focus on the practical part of the exam and there will be solved examples matching the written part of the exam.

Compulsory literature:

Trench, W: Introduction to Real Analysis. http://ramanujan.math.trinity.edu/wtrench/texts/index.shtml (free download)

Recommended literature:

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

The course is optional and requires the active participation of students registered. Participation on tutorials is obligatory, 20% of absence can be apologized.

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. 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: 2018/2019 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit Credit  
Mandatory attendence parzicipation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction K Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T049) Realization of Constructions K Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T036) Transport Constructions (01) Transport Constructions P Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T036) Transport Constructions (02) Traffic Engineering P Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T049) Realization of Constructions P Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T021) Building Materials and Diagnostics of Structures P Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner