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Ukončeno v akademickém roce 2020/2021

Methematics IV

Type of study Follow-up Master
Language of instruction Czech
Code 230-0204/01
Abbreviation MgrM4
Course title Methematics IV
Credits 4
Coordinating department Department of Mathematics
Course coordinator Mgr. Jitka Krčková, Ph.D.

Osnova předmětu

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.

Doporučená literatura

http://homen.vsb.cz/~kre40/matematika.html
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)