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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Functional analysis

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Code Completion Credits Range Language
D01FAN_EN ZK 1P+1S English
Garant předmětu:
Aleš Nekvinda
Lecturer:
Aleš Nekvinda
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

The lectures will be devoted to the study of Hilbert and Banach spaces and operators on them with regard to applications in the theory of partial differential equations. We say basic theorems of the functional analysis, Hahn-Banach's, Banach-Steinhaus's theorem, and the theorem on open mapping and on the closed graph. The concept of dual space and reflexivity, the quadratic functional, the theorem about the minimum and the relation with the operator equation have been introduced. Furthermore, we can prove Riesz's theorem on representation and Lax-Milgram's theorem. We will introduce a weak convergence and we will prove a weak compactness of the unit ball. We show that the convex continuous coercive functional in the reflexive Banach space has a minimum. Let's mention Browder's theorem about monotone operators. Finally, we will show applications on elliptical problems.

Requirements:
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Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
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The course is a part of the following study plans:
Data valid to 2024-05-27
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