M8202 Vybrané partie z matematické analýzy II

Faculty of Science
Spring 2002
Extent and Intensity
2/0/0. 3 credit(s). 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
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites (in Czech)
M5160 Differential Eqs.&Cont. Models || M6160 Differential Eqs.&Cont. Models
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
This course contains an exposition of fundamental results of the theory of boundary value problems for systems of linear and nonlinear differential equations. In particular, criteria are given for problems with functional, multi-point, and two-point boundary conditions to be solvable and well-posed, as well as methods of finding approximate solutions. It is also examine questions of existence, uniqueness, and stability of periodic and bounded solutions of nonautonomous differential systems.
Syllabus
  • §1. The general BVP 1.1. Unique solvability and well-posedness of a linear BVP 1.2. Criteria for existence and uniqueness of solutions of nonlinear BVP 1.3. Well-posedness for nonlinear BVP §2. Multi-point BVP 2.1 Statment of the main results 2.2. Existence criteria 2.3. Uniqueness and well-posedness 2.4. On a Method of constructing of solution §3. Two-point problems 3.1. Existence theorems 3.2. Uniqueness theorems and well-posedness 3.4. Two dimensional differential systems §4. Periodic BVP 4.1. Existence of periodic solution 4.2. Linear systems 4.3. Periodic solutions of nonlinear systems 4.4. Periodic solutions of two-dimensional systems §5. Bounded solutions 5.1. Existence and uniqueness theorems 5.2. Bounded solutions of two-dimensional systems
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2000.
  • Enrolment Statistics (recent)
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