PřF:M7180 Functional Analysis II - Course Information
M7180 Functional Analysis II
Faculty of ScienceAutumn 2015
- Extent and Intensity
- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Michal Veselý, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 8:00–9:50 M6,01011
- Timetable of Seminar Groups:
- Prerequisites
- M6150 Functional Analysis I
Differential and integral calculus. Linear 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
- Algebra and Discrete Mathematics (programme PřF, N-MA)
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)
- Statistics and Data Analysis (programme PřF, N-MA)
- 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. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in this subject area; to analyse selected problems from the topics of the course.
- Syllabus
- 1. Spectrum of linear operators (repetition from the course Functional analysis I).
- 2. Spectral theory of self-adjoint and symmetric operators.
- 3. Symmetric and self-adjoint operators in Hilbert spaces: Deficiency indices, self-adjoint extension of a symmetric operator.
- 4. Differential calculus in Banach spaces.
- 5. Strictly and uniformly convex spaces.
- 6. Integration of functions with values in Banach spaces.
- 7. Degree of a mapping on Banach spaces and its applications. Fixed point theorems.
- Literature
- recommended literature
- DRÁBEK, Pavel and Jaroslav MILOTA. Lectures on nonlinear analysis. 1. vyd. Plzeň: Vydavatelský servis, 2004, xi, 353. ISBN 8086843009. info
- STARÁ, Jana and Oldřich JOHN. Funkcionální analýza : nelineární úlohy. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 215 s. info
- Teaching methods
- lectures and class exercises
- Assessment methods
- Exam: oral. Requirements: to manage the theory from lectures and exercises.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught once in two years.
- Enrolment Statistics (Autumn 2015, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2015/M7180