PřF:M7160 Ord. Differential Equations II - Course Information
M7160 Ordinary Differential Equations II
Faculty of Sciencespring 2018
- 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. 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 - Timetable
- Tue 10:00–11:50 M2,01021
- Timetable of Seminar Groups:
- Prerequisites
- 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 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)
- 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.
- 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
- 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
- Literature
- recommended 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
- not specified
- 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
- Czech
- Further Comments
- The course is taught once in two years.
- Enrolment Statistics (spring 2018, recent)
- Permalink: https://is.muni.cz/course/sci/spring2018/M7160