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:
M0150/01: Thu 13:00–13:50 M4,01024, 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
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
    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
  • 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
    not specified
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1986. 896 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 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 2015, Spring 2017, Spring 2019, Spring 2021.
  • Enrolment Statistics (recent)
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