# PřF:M0150 Difference Equations - Course Information

## M0150 Difference Equations

**Faculty of Science**

Spring 2023

**Extent and Intensity**- 2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Taught online. **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**- Thu 11:00–12:50 M4,01024
- Timetable of Seminar Groups:

*P. Zemánek* **Prerequisites**- The basic course of Mathematical analysis I-II is supposed, the knowledges of differential equations may be 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.
**Learning outcomes**- Students will know applications of difference equations and understand theoretical and practical methods for their solution. 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: illustration of applications of difference equations (problems from discrete mathematics, Fibonacci sequence, discretization of ODE, etc.).
- II. Difference calculus: differences, basic rules, differences of "composition" of sequences, differences of "elementary" sequences, differences of polynomials and transformation of polynomials from classical powers to generalized powers, discrete analogies of theorems from differential calculus (Bolzano, l'Hospital = Stolz- Cesaro) and their applications, discrete Taylor theorem.
- III. Summation calculus: summation, basic rules, summation of "elementary" sequences, definite sum.
- IV. Difference equations: equations of the 1st order and their applications, linear equations of higher orders (derivation of the form of the solution of a homogeneous equation, method of variation of constants, method of undetermined coefficients) and their applications.

**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 and exercises.
**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**- The course is taught once in two years.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/spring2023/M0150