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Course detail

Sturm-Lieouville Theory

Course unit code: FSI-9SLT
Academic year: 2016/2017
Year of study: Not applicable.
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
Knowledge of basic topics of the spectral theory of second order differential operators and ability to apply this knowledge in practice.
Mode of delivery:
Not applicable.
Prerequisites:
Differential and integral calculus, ordinary differential equations.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
The course deals with basic topics of the Sturm-Lieouvill theory. The results are applied to solving of certain problems of mathematical analysis and engineering.
Recommended or required reading:
P. Hartman: Ordinary differential equations. Corrected reprint of the second (1982) edition [Birkhäuser, Boston, MA.]. Philadelphia, PA, 2002. xx+612 pp. ISBN: 0-89871-510-5 34-01 (37-01). (EN)
A. N. Kolmogorov, S. V. Fomin: Základy teorie funkcí a funkcionální analýzy, SNTL, Praha 1975. (CS)
E. C.Titchmarsh: Eigenfunction expansions associated with second-order differential equations. Part I. Second Edition Clarendon Press, Oxford 1962 vi+203 pp. (EN)
Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
Course-unit credit is awarded on condition of having attended the seminars actively and passed the control test.
Examination has a practical and a theoretical part. In the practical part student has to illustrate the given tasks on particular examples.
Theoretical part includes questions related to the subject-matter presented at the lectures.
Language of instruction:
Czech, English
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
The aim of the course is to familiarise students with basic topics and procedures of the Sturm-Lieouville theory in other mathematical subjects and applications.
Specification of controlled education, way of implementation and compensation for absences:
Absence has to be made up by self-study using recommended literature.

Type of course unit:

Lecture: 20 hours, optionally
Teacher / Lecturer: prof. Aleksandre Lomtatidze, DrSc.
Syllabus: 1. Second order ODE, Sturmian theory.
2. Two-point boundary value problém, Fredholm theorems.
3. Well-possedness of two-point BVP.
4. Eigenvalues and eigenfunctions.
5. Properties of eigenfunctions.
6. Completness of eigenfunctions.
7. Examples and applications.
8. Bessel and hypergeometric functions.
9. Second order equation on half-line, oscillation theory.
10. Spectrum of differential operator.

The study programmes with the given course