M7180 Functional Analysis II

Faculty of Science
Autumn 2023
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Peter Šepitka, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Mon 11:00–11:50 M3,01023, P. Šepitka
Prerequisites
M6150 Functional Analysis I
Differential and integral calculus. Functional analysis I.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Functional analysis belongs to fundamental parts of university courses in mathematics. It is utilized by a number of other courses and in many applications. The main aim of the course is to explain bases of the theory of linear operators and the derivative in Banach spaces.
Learning outcomes
At the end of the course students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • 0. Linear operators (repetition from the course Functional analysis I).
  • 1. Compact operators.
  • 2. Differential calculus in Banach spaces.
  • 3. Strictly and uniformly convex spaces.
  • 4. Degree of a mapping on Banach spaces. Fixed point theorems.
  • 5. Integration of functions with values in Banach spaces.
Literature
    recommended literature
  • DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis. xi, 353. ISBN 8086843009. 2004. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury. 581 s. 1975. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum. 106 s. ISBN 802460969X. 2005. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum. 354 s. ISBN 8071845973. 2002. info
  • NAJZAR, Karel. Funkcionální analýza. Vyd. 1. Praha: Státní pedagogické nakladatelství. 183 s. 1975. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství. 215 s. 1986. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. Vyd. 1. Praha: Academia. 408 s. 1973. URL info
Teaching methods
Lectures, seminars
Assessment methods
Two-hour written final exam (it is needed to reach at least 50 % of points) with oral evaluation of the exam with each student.
The conditions (especially regarding the form of the exam) will be specified according to the epidemiological situation and valid restrictions.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/M7180