457-0303/01 – Introduction to functional analysis and variational methods (UFAVM)

Gurantor department	Department of Applied Mathematics	Credits	6
Subject guarantor	prof. RNDr. Jiří Bouchala, Ph.D.	Subject version guarantor	prof. RNDr. Jiří Bouchala, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	2	Semester	winter
		Study language	Czech
Year of introduction	2003/2004	Year of cancellation	2009/2010
Intended for the faculties	FEI	Intended for study types	Follow-up Master

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	4+2
Part-time	Credit and Examination	4+2

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

Compulsory literature:

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:

Přednášky: Úvod do funkcionální analýzy: Metrický prostor. Úplný metrický prostor. Banachův prostor. Lineární funkcionály. Slabá konvergence. Hilbertův prostor. Operátory v Banachových a Hilbertových prostorech. Gateauxův a Fréchetův diferenciál a derivace. Extrémy a kritické body funkcionálů. Variační metody: Lebesgueův integrál. Prostory L^p(Omega). Zobecněné funkce (distribuce), zobecněné derivace. Sobolevovy prostory. Stopy funkcí na hranici. Slabá řeąení okrajových úloh. Existence a jednoznačnost slabého řeąení. Regularita slabého řešení. Funkcionál energie. Spektrum.

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 (145)	51	3
Examination	Examination	100	0	3
Exercises evaluation	Credit	45	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	(N2646) Information Technology	(1103T021) Computational Mathematics			P	Czech	Ostrava	2			Compulsory	study plan
2003/2004	(N2646) Information Technology	(1103T021) Computational Mathematics			K	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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