Course: Functional Analysis 1

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Course title Functional Analysis 1
Course code KMA/FA1M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study 3
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Ludvík Pavel, RNDr. Ph.D.
  • Vodák Rostislav, doc. RNDr. Ph.D.
Course content
1. Motivation and application of functional analysis (quantum physics, modern methods of mathematical physics) 2. Metric spaces, normed linear spaces, Banach and Hilbert spaces and their properties 3. Operators, spectrum, space of continuous linear operators, dual spaces, reflexivity 4. Orthonormal bases and projections. Riesz theorem. 5. Hahn-Banach theorem and its consequences. 6. Compactness and weak converegence.

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training), Demonstration
  • Attendace - 52 hours per semester
  • Preparation for the Course Credit - 30 hours per semester
  • Homework for Teaching - 30 hours per semester
  • Preparation for the Exam - 70 hours per semester
Learning outcomes
Master basic methods and tools of linear functional analysis.
Comprehension Understand the mathematical theory of linear operators in linear spaces and their applications.
Prerequisites
Understanding the basic elements of mathematical analysis including the mathematical tools of differential and integral calculus.

Assessment methods and criteria
Oral exam, Written exam

Written test and oral exam. Credit: active participation and written test.
Recommended literature
  • A. Sasane. (2017). Friendly Approach To Functional Analysis. WSPC.
  • B. D. Reddy. (1998). Introductory Functional Analysis: With Applications to Boundary Value Problems and Finite Elements.
  • E. Kreyszig. (1989). Introductory Functional Analysis with Applications.
  • E. Zeidler. (1999). Applied Functional Analysis, Applications to Mathematical Physics.
  • E. Zeidler. (1995). Applied Functional Analysis, Main Principles and Their Applications.
  • J. Lukeš. (2001). Zápisky z funkcionální analýzy.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): General Physics and Mathematical Physics (2019) Category: Physics courses 3 Recommended year of study:3, Recommended semester: Winter