M0150 Difference Equations

Faculty of Science
Spring 2015
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)
prof. RNDr. Roman Šimon Hilscher, DSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
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 offered to students of any study field.
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.
The last part devoted to the oscillation theory of difference equations may serve as a preparation for a research activity in this field.
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
  • 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
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. Minimum 50% of attendance of lectures is required.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2003, Spring 2005, Spring 2007, Spring 2009, Spring 2011, Spring 2013, Spring 2017, Spring 2019, Spring 2021, Spring 2023, Spring 2025.
  • Enrolment Statistics (Spring 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2015/M0150