457-0304/01 – Nonlinear Functional Analysis (NEFN)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year2Semestersummer
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

Successful student will gain basic knowledge of nonlinear functional analysis and its applications.

Teaching methods

Lectures
Tutorials

Summary

The subject contains basic concepts of nonlinear functional analysis (compact operators, implicit function theorem, topological degree, monotone operators).

Compulsory literature:

E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.

Recommended literature:

Way of continuous check of knowledge in the course of semester

Podmínky udělení zápočtu: Aktivní účast na cvičeních. Vyřešení zadaných problémů.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Spektrální teorie lineárních operátorů: Samoadjungované operátory. Kompaktní operátory. Základní věty nelineární funkcionální analýzy: Věta o implicitní funkci. Věta o vázaných extrémech. Absolutní extrémy nelineárních funkcionálů: Existenční věty pro absolutní extrémy. Přibližné metody hledání minima funkcionálů. Nelineární operátorové rovnice a jejich řešení: Variační metoda řešení nelineárních rovnic. Teorie monotónních operátorů. Věty o pevném bodě. Teorie stupně zobrazení. Cvičení: Opakování prostorů funkcí a základních vlastností lineárních operátorů. Příklady samoadjungovaných a kompaktních operátorů. Věta o implicitní funkci a její aplikace. Aplikace věty o vázaných extrémech. Globální extrémy funkcionálů - důkaz jejich existence, přibližné metody pro jejich nalezení. Řešení nelineárních rovnic. Aplikace různých metod (variační metoda, monotónní operátory, věty o pevném bodě, stupeň zobrazení).

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Examination Examination 70  0
        Exercises evaluation Credit 30  10
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Choice-compulsory study plan
2007/2008 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2007/2008 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Choice-compulsory study plan
2006/2007 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 2 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 2 Optional study plan
2006/2007 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2649) Electrical Engineering (2601T004) Measurement and Control Engineering K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2005/2006 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems P Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2004/2005 (N2645) Electrical Engineerong, Communication and Computer Systems (2612T041) Control and Informatics Systems K Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner