470-6101/02 – 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 type B
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEI, USPIntended for study typesDoctoral
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 Examination 28+0
Part-time Examination 28+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

Other requirements

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: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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