M8180 Nonlinear Functional Analysis

Faculty of Science
Spring 2010
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18:00–19:50 MS2,01022
Prerequisites
M6150 Linear Functional Analysis I
Differential and integral calculus, Linear functional analysis I and II, Linear algebra.
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
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
Nonlinear functional analysis belongs to advanced parts of university courses in mathematics. It is utilized in many applications. The aim of the course is to introduce the bases of nonlinear functional analysis, namely differential and integral calculus in normed spaces and their applications. 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 these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • 1. Differential calculus in normed spaces. Freschet and Gateaux differentials. Integral calculus in normed spaces. Newton-Leibnitz formula. Higher order derivatives. Taylor formula. 2. Application of differential calculus. 3. Degree theory.
Literature
  • Lang, S. Real and Functional Analysis. Third Edition. Springer-Verlag 1993.
  • ZEIDLER, Eberhard. Nonlinear functional analysis and its applications. Translated by Leo F. Boron. New York: Springer-Verlag, 1990, xv, 469-12. ISBN 354097167X. 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, 1975, 581 s. info
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, seminar 1 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008.
  • Enrolment Statistics (recent)
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