PřF:M5160 Ord. Differential Equations I - Course Information
M5160 Ordinary Differential Equations I
Faculty of ScienceAutumn 2019
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- doc. RNDr. Josef Kalas, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 8:00–9:50 M4,01024
- Timetable of Seminar Groups:
- Prerequisites
- M3100 Mathematical Analysis III && M2110 Linear Algebra II
Mathematical analysis: Differential calculus of functions of one and several variables, integral calculus, sequences and series of numbers and functions, metric spaces, complex function of a real variable. Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. - 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
- Mathematics (programme PřF, N-MA)
- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)
- Course objectives
- The theory of differential equations ranks among fundamental parts of mathematical analysis. It is utilized by a number of other courses and in many applications. The basic aim of the course is to familiarize students with the fundamentals of the theory of ordinary differential equations, with the basic parts of the stability and qualitative theory of differential equations and to show connections with other parts of mathematics.
- Learning outcomes
- After passing the course, the student will be able:
to define and interpret the basic notions used in the fields mentioned above;
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques utilized in these subject areas;
to apply acquired pieces of knowledge for the solution of specific problems. - Syllabus
- 1. Fundamental notions - ordinary differential equations and their systems, order of an equation, initial value problem, solutions of differential equations and initial value problems. 2. Systems of linear differential equations - existence and uniqueness of solutions, structure of the family of solutions, variation-of-constants method, linear systems with constant coefficients, connection of linear systems with higher-order linear differential equations. 3. Local and global properties of solutions - local existence and uniqueness of solutions of nonlinear initial value problems, global existence and uniqueness, dependence of solutions on initial values and parameters. 4. Introduction to the stability theory - Lyapunov concept of stability, uniform, asymptotic and exponential stability, stability of linear and perturbed linear systems, Hurwitz criterion, direct method of Lyapunov.
- Literature
- required literature
- KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). Vyd. 3. Brno: Masarykova univerzita, 2012, 207 s. ISBN 9788021058156. info
- recommended literature
- 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
- GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
- RÁB, Miloš. Metody řešení diferenciálních rovnic. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1989, 68 s. info
- RÁB, Miloš. Metody řešení diferenciálních rovnic. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1989, 61 s. info
- not specified
- Hartman, Philip. Ordinary differential equations. Wiley, New York-London-Sydney, 1964.
- Coppel, W. A. Stability and asymptotic behaviour of differential equations. D. C. Heath and company, Boston, 1965.
- Teaching methods
- lectures and class exercises
- Assessment methods
- One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of four exercises. It is necessary to obtain at least 1,5 from possible 4 points.
- Language of instruction
- Czech
- Follow-Up Courses
- Further comments (probably available only in Czech)
- The course is taught annually.
- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2019/M5160