MD138 Half-linear equations

Faculty of Science
Spring 2019
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Petr Hasil, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Petr Hasil, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Mon 18:00–19:50 M2,01021
Prerequisites
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, metric spaces
Linear algebra: Systems of linear equations, linear spaces, linear transformations and matrices, canonical form of a matrix
Differential equations: Linear and non-linear systems of ordinary differential equations
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 course is focused on half-linear differential and difference equations of the Euler type. The following questions are studied in detail: the oscillation, the non-oscillation, and the Riccati method.
Learning outcomes
At the end of the course, students will be able to:
define and interpret the basic notions used in the mentioned fields;
formulate relevant mathematical theorems and statements and to explain methods of their proofs;
use effective techniques utilized in the subject areas;
analyse selected problems from the topics of the course.
Syllabus
  • Linear and half-linear differential and difference equations of the second order
  • The Sturm theory
  • Oscillation and non-oscillation of Euler type equations
  • The Riccati method
  • Conditional oscillation and critical oscillation constant
  • Dynamical equations on time scales
Literature
    required literature
  • DOŠLÝ, Ondřej and Pavel ŘEHÁK. Half-linear differential equations. Online. 1st ed. Amsterdam: Elsevier, 2005. xiv, 517. ISBN 0444520392. [citováno 2024-04-24] info
    recommended literature
  • ŘEHÁK, Pavel. A Riccati technique for proving oscillation of a half-linear equation. Online. Electronic Journal of Differential Equations. San Marcos, TX 78666, USA: Texas State University - San Marcos, 2008, vol. 2008, No 105, p. 1-8. ISSN 1072-6691. [citováno 2024-04-24] URL info
  • DOŠLÝ, Ondřej and Petr HASIL. Critical oscillation constant for half-linear differential equations with periodic coefficients. Online. Annal. Mat. Pura Appl. 2011, vol. 190, No 3, p. 395-408. ISSN 0373-3114. [citováno 2024-04-24] info
  • DOŠLÝ, Ondřej. A Linearization Technique in Half-Linear Oscillation Theory. Online. In Topological Methods, Differential Equations, and Dynamical Systems. 2007, [citováno 2024-04-24] info
  • ŘEHÁK, Pavel. A critical oscillation constant as a variable of time scales for half-linear dynamic equations. Online. Mathematica Slovaca. Bratislava: Slovak Academy of Sciences, 2010, vol. 60, No 2, p. 237-256. ISSN 0139-9918. Available from: https://dx.doi.org/10.2478/s12175-010-0009-7. [citováno 2024-04-24] info
    not specified
  • HARTMAN, Philip. Ordinary differential equations. Online. 2nd ed. Philadelphia, Pa.: SIAM, 2002. xx, 612 s. ISBN 0-89871-510-5. [citováno 2024-04-24] info
Teaching methods
Lectures
Assessment methods
The final oral exam (60 minutes) for 20 points. For successfull examination (the grade at least E), the student needs 10 points or more.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught only once.
Teacher's information
In the course, students have to solve the given research problems
  • Enrolment Statistics (recent)
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