Functional analysis - O02310052
Title: Funkcionální analýza
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: winter
E-Credits: 5
Examination process: winter s.:
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unknown / unknown (999)
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: full-time
Explanation: Rok3Student zapíše jeden z kurzů Funkce více proměnných nebo Metody matematické anal
Old code: FUAN
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Classification: Mathematics > Real and Complex Analysis
Pre-requisite : O0231SOUB
Opinion survey results   Examination dates   Schedule   Noticeboard   
Annotation -
Metric space, linear space, normed space, Banach and Hilbert space. Linear functionals, linear operators
Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Aim of the course -

To acquaint students with fundamental notions of topology and functional analysis

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Literature -

Edwards, R.E.: Functional Analysis,Rinehart and Wiston, New York 1965

Taylor, A.E.: Introduction to Functional Aanalysis

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Teaching methods -

Lecture and seminar

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Requirements to the exam -

Seminar:

  • regular attendance
  • correct elaboration of homeworks
  • passing the current tests

Exam:

  • mastering of definitions, theorems and proofs, ability to illustrate them by examples and counterexamples
  • mastering of methods of calculation of primitive functions and integrals and ability to apply them to solving of problems
Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)
Syllabus -

Spaces: metric, linear, normed, Banach, Hilbert.

Neighborhoods, open and closed sets. Convergence in metricspaces. Bolzano-Cauchy condition, completeness, separability.

Scalar product, orthogonality.

Linear functionals, Hahn-Banach theorem, adjoint space. Linear operators.

Last update: JARNIK/PEDF.CUNI.CZ (01.04.2009)