714-0504/01 – Mathematics IV - AFM (MIVAF)

Gurantor department	Department of Mathematics and Descriptive Geometry	Credits	5
Subject guarantor	RNDr. Jiří Poláček, CSc.	Subject version guarantor	RNDr. Jiří Poláček, CSc.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	2	Semester	summer
		Study language	Czech
Year of introduction	1999/2000	Year of cancellation	2005/2006
Intended for the faculties	HGF	Intended for study types	Master

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	3+2

Subject aims expressed by acquired skills and competences

This course is closed.

Teaching methods

Summary

The three-dimensional integral. Fubini’s theorem. Transformation into cylindrical and spherical coordinates. Applications. The surface integrals of the 1st and the 2nd kind. Gauss’ theorem. Stokes’ theorem. Applications. Basic terms of the field theory. The field of scalars and the field of vectors. The potential gradient. The divergence and rotation of the field of vectors. The Laplacian operator of the field of vectors. The Hamiltonian operator. The flow of the field of vectors through a surface segment. Systems of linear differential equations with constant coefficients. The method of elimination and Euler’s method. Fourier series. Fourier coefficients, Fourier series convergence. The function of a complex variable (FCV). Limit, continuity and derivation. The integral calculus of FCV.

Compulsory literature:

Škrášek, J. - Tichý, Z.: Základy aplikované matematiky II. SNTL, Praha 1986 Vlček, J. - Vrbický, J.: Matematika IV. Diferenciální rovnice. Skriptum VŠB-TU. Ostrava 1997 Častová, N. - Vlček, J.: Funkce komplexní proměnné a integrální transformace. Skriptum VŠB-TU. Ostrava 1992

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (100)	51	3
Exercises evaluation	Credit	20 (20)	0	3
Project	Project	5	0	3
Written exam	Written test	10	0	3
Other task type	Other task type	5	0	3
Examination	Examination	80 (80)	0	3
Written examination	Written examination	60	0	3
Oral	Oral examination	20	0	3

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 year	Programme	Branch/spec.	Spec.	Zaměření	Form	Study language	Tut. centre	Year	W	S	Type of duty
2003/2004	(M2102) Mineral Raw Materials	(3911T001) Applied Physics of Materials			P	Czech	Ostrava	2			Compulsory	study plan
2002/2003	(M2102) Mineral Raw Materials	(3911T001) Applied Physics of Materials			P	Czech	Ostrava	2			Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

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