470-4111/04 – Introduction to Functional Analysis (ÚFA)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | prof. RNDr. Jiří Bouchala, Ph.D. | Subject version guarantor | prof. RNDr. Jiří Bouchala, Ph.D. |
Study level | undergraduate or graduate | Requirement | Choice-compulsory |
Year | 1 | Semester | winter |
| | Study language | English |
Year of introduction | 2016/2017 | Year of cancellation | 2020/2021 |
Intended for the faculties | USP | Intended for study types | Follow-up Master |
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
Tutorials
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:
E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.
Way of continuous check of knowledge in the course of semester
Podmínky udělení zápočtu:
Aktivní účast na cvičeních. Vyřešení zadaných problémů.
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.
Local and Global Extremes.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.