PřF:M0150 Difference Equations - Course Information
M0150 Difference Equations
Faculty of ScienceSpring 2025
- Extent and Intensity
- 2/1/0. 3 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
- doc. Mgr. Petr Zemánek, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - 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 first order and their applications, dynamics of difference equations of the first order (Sharkovskii theorem and bifurcations), 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, Sturm-Liouville difference equation of the second order and eigenvalue problem.
- Literature
- recommended 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
- RADIN, Michael A. Difference Equations for Scientists and Engineering: Interdisciplinary Difference Equations. New Jersey: World Scientific, 2019. ISBN 978-981-12-0385-5. 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
- ELAYDI, Saber N. Discrete chaos. Boca Raton: Chapman & Hall/CRC, 2000, xiii, 355. ISBN 1-58488-002-3. info
- An introduction to difference equations. Edited by Saber N. Elaydi. 3rd ed. New York: Springer, 2005, xxii, 539. ISBN 0387230599. info
- PRÁGEROVÁ, Alena. Diferenční rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1971, 115 s. URL info
- 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.
The course is taught: every week.
- Enrolment Statistics (Spring 2025, recent)
- Permalink: https://is.muni.cz/course/sci/spring2025/M0150