470-6101/01 – Applied Functional Analysis (APFA)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesUSP, FEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
HAS35 prof. RNDr. Jaroslav Haslinger, DrSc.
KRU14 prof. Ing. Jaroslav Kruis, Ph.D.
LAM05 doc. RNDr. Marek Lampart, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 2+0
Combined Examination 10+0

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
Project work

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:

P. Drábek, J. Milota: Methods of Nonlinear Analysis, Birkhauser Advanced Texts, Berlin, 2007

Way of continuous check of knowledge in the course of semester

Individual work.

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. - Extrema of functionals, critical points.

Conditions for subject completion

Full-time form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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2019/2020 (P0713D060002) Electrical Engineering Science P Czech Ostrava Choice-compulsory type B study plan
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2019/2020 (P0613D140005) Computer Science K Czech Ostrava Choice-compulsory type B study plan
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2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
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2017/2018 (P2658) Computational Sciences (2612V078) Computational Sciences P Czech Ostrava Choice-compulsory study plan
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2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2658) Computational Sciences (2612V078) Computational Sciences P Czech Ostrava Choice-compulsory study plan
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2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P Czech Ostrava Choice-compulsory study plan
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2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan
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2011/2012 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
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2010/2011 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
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2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2010/2011 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K Czech Ostrava Choice-compulsory study plan

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