Course detail

Sturm-Lieouville Theory

FSI-9SLT Acad. year: 2022/2023 Winter semester

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.

Language of instruction

Czech

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.

Prerequisites

Differential and integral calculus, ordinary differential equations.

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.

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.

The study programmes with the given course

Programme D-APM-P: Applied Mathematics, Doctoral, recommended course

Programme D-APM-K: Applied Mathematics, Doctoral, recommended course

Type of course unit

 

Lecture

20 hours, optionally

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.