M8960 Topological methods in nonlinear analysis

Faculty of Science
Spring 2009
Extent and Intensity
2/0. 2 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
Tue 15:00–16:50 MS2,01022
Prerequisites
Differential and integral calculus.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The aim of the course is to present bases of the topological degree theory and to apply them to nonlinear analysis. 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
  • Vector field. Angular function. Rotation number. The Poincaré formula. Calculation. Odd vector field. Tangential field. Singular points. Index. Algebraic number of singular points. Homotopy theory. Degree theory. Applications. Fixed point theorems. Poles of analytic functions. Solvability of nonlinear systems. Linear and nonlinear boundary value problems. Multiplicity results. The Poincaré-Bendixson theory.
Literature
  • Krasnosel'skij, M. A., Perov, A. I., Povolockij, A. I., Zabrejko, P. P., Vektornye polya na ploskosti, Moskva, 1963
  • KRASNOSEL‘SKIJ, Mark Aleksandrovič. Topologičeskijje metody v teorii nelinejnych integral'nych uravnenij. Moskva: Techniko teoretičeskoj literatury, 1956, 392 s. info
Teaching methods
lectures
Assessment methods
Teaching: lecture 2 hours a weak. Exam: oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught only once.
The course is also listed under the following terms Spring 2007.
  • Enrolment Statistics (recent)
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