M7160 Ordinary Differential Equations II

Faculty of Science
Spring 2014
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Fri 13:00–14:50 M6,01011
  • Timetable of Seminar Groups:
M7160/01: Fri 15:00–15:50 M6,01011, M. Veselý
M5160 Ord. Differential Equations I
Mathematical analysis: Differential calculus of functions of several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex functions of a real variable.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformations and matrices, canonical form of a matrix.
Differential equations: Linear and non-linear systems of ordinary differential equations, stability theory, autonomous equations.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course is focused on systems of non-linear differential equations with the Carathéodory right-hand side. The following questions are studied in detail: the existence of solutions of the Cauchy problem; the extendibility of solutions; and the existence of global solutions. At the end of the course, students should be able to formulate relevant mathematical theorems and their proofs, to use effective techniques utilized in these subject areas, and to analyse selected problems from the topics of the course.
  • The Carathéodory class of functions
  • Absolutely continuous functions
  • The Carathéodory theorem for higher-order differential equations
  • Extendibility of solutions of the Cauchy problem
  • Lower and upper solutions of the Cauchy problem
  • Set of solutions of the Cauchy problem
  • Differential and integral inequalities
  • Global solutions of the Cauchy problem
  • Uniqueness of solutions of the Cauchy problem
    required literature
  • HARTMAN, Philip. Ordinary differential equations. 2nd ed. Philadelphia, Pa.: SIAM, 2002. xx, 612 s. ISBN 0-89871-510-5. info
  • CODDINGTON, Earl A. and Norman LEVINSON. Theory of ordinary differential equations. New York: McGraw-Hill, 1955. 429 s. info
  • KIGURADZE, Ivan. Okrajové úlohy pro systémy lineárních obyčejných diferenciálních rovnic. 1. vyd. Brno: Masarykova univerzita, 1997. 183 s. ISBN 80-210-1664-7. info
    recommended literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 2. vyd. Brno: Masarykova univerzita, 2001. 207 s. ISBN 8021025891. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978. 418 s. info
Teaching methods
Lectures, seminars
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
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, Autumn 2000, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2016, spring 2018, Spring 2020, Spring 2022.
  • Enrolment Statistics (Spring 2014, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2014/M7160