470-4111/01 – Introduction to Functional Analysis (ÚFA)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
VOD03 Mgr. Petr Vodstrčil, 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

The course aims at introducing the students in fundamentals of functional analysis. In order to solve a number of technical problems, it is necesarry to master this (rather technical) discipline.

Teaching methods

Lectures
Tutorials

Summary

Within the course the students will be introduced in fundamental notions of functional analysis, which is a subject unifying results and methods of many classical mathematical disciplines (algebra, geometry, calculus). It identifies and emphasizes what they have in common and, further, it generalizes them. Functional analysis is involved in various parts of mathematics and its applications and it provides tools enabling to formulate as well as solve complex practical problems. The introduced abstract notions will be demonstrated at examples and applications.

Compulsory literature:

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

Recommended literature:

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

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

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Metric Space. Complete Metric Space. Banach Fixed Point Theorem. Banach Space. Linear Functionals. Weak Convergence . Hilbert Space. Riesz Theorem. Operators in Banach and Hilbert Spaces Gateaux Derivative. Fréchet Derivative. Local and Global Extremes.

Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter 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
        Exercises evaluation Credit 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Compulsory study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner