# PřF:M0150 Difference Equations - Course Information

## M0150 Difference Equations

**Faculty of Science**

Spring 2017

**Extent and Intensity**- 2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
**Teacher(s)**- doc. Mgr. Petr Zemánek, Ph.D. (lecturer)
**Guaranteed by**- prof. RNDr. Roman Šimon Hilscher, DSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 20. 2. to Mon 22. 5. Mon 10:00–11:50 MS1,01016
**Prerequisites**- The basic course of Mathematical analysis I-II is supposed, the knowledges of differential equations are useful.
**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**- Mathematical Analysis (programme PřF, N-MA)
- Mathematical Modelling and Numeric Methods (programme PřF, N-MA)

**Course objectives**- The aim of the course is to present the basic facts of the theory of difference equations. Students will understand theoretical and practical methods for solving difference equations.

Students will be able to compare the differences in the theories of differential and difference equations and, in particular, understand the differences which arise in these theories. **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**- KELLEY, Walter G. and Allan C. PETERSON.
*Difference equations : an introduction with applications*. 2nd ed. San Diego: Academic Press, 2001. ix, 403. ISBN 9780124033306. info - AGARWAL, Ravi P.
*Difference equations and inequalities : theory, methods, and applications*. 2nd ed., revised and expande. New York: Marcel Dekker, 2000. xiii, 971. ISBN 0824790073. info *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

*recommended literature*- KELLEY, Walter G. and Allan C. PETERSON.
**Teaching methods**- Lectures about theory with illustrative solved problems.
**Assessment methods**- Two-hour written final exam (it is needed to reach at least 50% of points) with oral evaluation of the exam with each student.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (Spring 2017, recent)
- Permalink: https://is.muni.cz/course/sci/spring2017/M0150