Course: Functional Analysis 2

« Back
Course title Functional Analysis 2
Course code KMA/FA2N
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Staněk Svatoslav, prof. RNDr. CSc.
  • Pastor Karel, doc. Mgr. Ph.D.
Course content
1. The Closed graph theorem. 2. The uniform boundedness principle. 3. Reflexive spaces. 4. The Eberlein-Šmulian theorem. 5. The Brouwer fixed point theorem. 6. Completely continuous operators. 7. The Schauder fixed point theorem and its consequences. 8. The Brouwer degree of operators. 9. Fixed point theorems in partially ordered spaces. 10. Differential calculus in normed linear spaces (Gâteaux and Fréchet derivative of operators). 11. The Implicit function theorem. 12. Spectral theory of linear and linear continuous operators in normed linear spaces and product spaces. 13. Spectral theory of linear completely continuous operators and symmetric linear completely continuous operators in normed linear spaces and product spaces.

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
  • Attendace - 39 hours per semester
  • Preparation for the Course Credit - 10 hours per semester
  • Preparation for the Exam - 40 hours per semester
Learning outcomes
Understand the principles of functionaal analysis and fixed point theorems.
Comprehension Understand the principles of functional analysis, spectral theory and fixed point theorems.
Prerequisites
Basic notions of functional analysis.

Assessment methods and criteria
Oral exam, Dialog

Credit: active participation, homework solving. Exam: the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • J. Lukeš. (2001). Zápisky z funkcionální analýzy. MatFyzPress.
  • K. Deimling. (1985). Nonlinear functional analysis. Springer.
  • K. Najzar. (1988). Funkcionální analýza. SPN, Praha.
  • M. Fabian a kol. (2001). Functional Analysis and Infinite-Dimensional Geometry. Springer New York.
  • P. Drábek, J. Milota. (2004). Lectures on Nonlinear Analysis. Plzeň.
  • Taylor, A. E. (1977). Úvod do funkcionální analýzy. Academia, Praha.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 2 Winter
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Winter
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses - Winter