Czech

Not applicable.

Knowledge of basic topics of the metric, linear, normed and unitary spaces, Lebesgue integral
and ability to apply this knowledge in practice.

Differential and integral calculus, numerical methods, ordinary differential equations.

Not applicable.

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Course-unit credit is awarded on condition of having attended the seminars actively and passed the control test.
Examination has a practical and a theoretical part. In the practical part student has to illustrate the given tasks on particular examples.
Theoretical part includes questions related to the subject-matter presented at the lectures.

1. Metric spaces - definition and examples, classification of subsets, separability, covergence, completness, compactness, compactness of sets in particular spaces.
2. Measura theory - Lebesgue measure, measurable functions, Lebesgue integral, Lebesgue dominant theorem.
3. Linear spaces - definition and examples, normed space, Euclidian space, Bessel inequality, Riesz-Fischer theorem, Hilbert space, characteristic property of Euclidian spaces.
4. Functionals - definition and examples, geometric interpretation, convex sets, convex functionals, Hahn-Banach theorem, continuous linear functionals, Hahn-Banach theorem in normed spaces.
5. Adjoint spaces - definition and examples, second adjoint spaces, weak convergence, Banach-Steinhaus theorem, weak convergence and bounded sets in adjoint spaces.

Not applicable.

The aim of the course is to familiarise students with basic topics and procedures of the functional analysis used in other mathematical subjects.

Absence has to be made up by self-study using recommended literature.

Not applicable.

Not applicable.

A. N. Kolmogorov, S. V. Fomin: Základy teorie funkcí a funkcionální analýzy, SNTL, Praha 1975. (CS)
C. Costara, D. Popa, Exercises in functional analysis, Kluwer 2003. (EN)
D. H. Griffel, Applied functional analysis, Dover 2002. (EN)
E. Zeidler, Applied functional analysis: Main principles and their applications, Springer, 1995. (EN)
F. Burk, Lebesgue measure and integration: An introduction, Wiley 1998. (EN)
J. Franců, Funkcionální analýza 1, FSI VUT 2014. (CS)
J. Lukeš, Zápisky z funkcionální analýzy, Karolinum 1998. (CS)

Not applicable.