M7180 Functional Analysis II

Faculty of Science
Autumn 2019
Extent and Intensity
2/1/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Peter Šepitka, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Thu 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7180/01: Mon 8:00–8:50 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, 2004. xi, 353. ISBN 8086843009. info
  • KOLMOGOROV, A. N. and S. V. FOMIN. Základy teorie funkcí a funkcionální analýzy. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1975. 581 s. info
  • LUKEŠ, Jaroslav. Úvod do funkcionální analýzy. 1. vyd. Praha: Karolinum, 2005. 106 s. ISBN 802460969X. info
  • LUKEŠ, Jaroslav. Zápisky z funkcionální analýzy. 1. vyd. Praha: Karolinum, 2002. 354 s. ISBN 8071845973. info
  • NAJZAR, Karel. Funkcionální analýza. 1. vyd. Praha: Státní pedagogické nakladatelství, 1975. 183 s. info
  • STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. 1. vyd. Praha: Státní pedagogické nakladatelství, 1986. 215 s. info
  • TAYLOR, Angus E. Úvod do funkcionální analýzy. 1. vyd. Praha: Academia, 1973. 408 s. info
Teaching methods
Lectures, seminars
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
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.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2019/M7180