# PřF:M0150 Difference Equations - Course Information

## M0150 Difference Equations

**Faculty of Science**

Spring 2003

**Extent and Intensity**- 2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Ondřej Došlý, DrSc. (lecturer)
**Guaranteed by**- prof. RNDr. Ondřej Došlý, DrSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Contact Person: prof. RNDr. Ondřej Došlý, DrSc. **Prerequisites**- The basic course of Mathematical analysis I-III is supposed, the knowledges of the courses Differential Equations and Continuous Models (M ...) are useful and the knowledges of the course Ordinary Differential Equations II can make no harm.
**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)

**Course objectives**- The aim of the course is to present the basic facts of the theory of difference equations. The last part devoted to the oscillation theory of difference equations may serve as a preparation for a research activity in this field.
**Syllabus**- I. Introduction: motivation, elements of the diference calculus, elementary recursions. II. Linear difference systems: homogeneous and nonhomogeneous systems, variation of parameters, transformations of difference systems, higher order linear difference equations. III. Stability of difference equations and systems: motivation, dynamics of first order difference equations, stability of linear equations and systems. IV. Oscillation theory of difference equations: Sturm-Liouville second order difference equation, methods of discrete oscillation theory, symplectic difference systems, difference equations and orthogonal polynomials.

**Literature***An introduction to difference equations*. Edited by Saber N. Elaydi. 2nd ed. New York: Springer-Verlag, 1999. xvi, 427. ISBN 0387988300. info- PRÁGEROVÁ, Alena.
*Diferenční rovnice*. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1971. 115 s. URL info - ŠKRÁŠEK, Josef and Zdeněk TICHÝ.
*Základy aplikované matematiky.*Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1986. 896 s. URL info

**Assessment methods**(in Czech)- Přednáška bez cvičení, zakončena ústní zkouškou.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course is taught once in two years.

The course is taught: every week.

- Enrolment Statistics (Spring 2003, recent)
- Permalink: https://is.muni.cz/course/sci/spring2003/M0150