|
Lecturer(s)
|
-
Vodák Rostislav, doc. RNDr. Ph.D.
-
Tomeček Jan, 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), Dialogic Lecture (Discussion, Dialog, Brainstorming)
|
|
Learning outcomes
|
Master basic methods and tools of linear functional analysis.
Comprehension Understand the mathematical theory of linear operators in linear spaces.
|
|
Prerequisites
|
Understanding the basic elements of mathematical analysis including the mathematical tools of differential and integral calculus.
KMA/MA1 and KMA/MA2 and KMA/MA3 and KAG/LA1A
|
|
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. Springer.
-
E. Kreyszig. (1989). Introductory Functional Analysis with Applications. Wiley.
-
E. Zeidler. (1999). Applied Functional Analysis, Applications to Mathematical Physics. Springer.
-
E. Zeidler. (1995). Applied Functional Analysis, Main Principles and Their Applications. Springer.
-
J. Lukeš. (2001). Zápisky z funkcionální analýzy. Matfyzpress, Praha.
|