230-0230/01 – Selected applications of mathematics (VAVM)

 Gurantor department Department of Mathematics Credits 2 Subject guarantor Mgr. Marcela Jarošová Subject version guarantor Mgr. Marcela Jarošová Study level undergraduate or graduate Requirement Optional Year Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FAST Intended for study types Bachelor, Follow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
JAR71 Mgr. Marcela Jarošová
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Graded credit 0+3
Part-time Graded credit 0+16

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

Individual consultations
Tutorials

Summary

Integral calculus of functions of several independent variables: double and triple integrals, 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.

Other requirements

There are no other requirements.

Prerequisities

Subject codeAbbreviationTitleRequirement
230-0201 BcM1 Mathematics Recommended
230-0202 BcM II Mathematics II Recommended

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. 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: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Graded credit Graded credit 100  51
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).

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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner