M7160 Ordinary Differential Equations II

Faculty of Science
Autumn 2002
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. Alexander Lomtatidze, DrSc.
Prerequisites
M5160 Differential Eqs.&Cont. Models
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. Differential equations: Linear and nonlinear systems of ordinary differential equations, existence, uniqueness and properties of solutions, elements of the 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
  • Mathematics (programme PřF, M-MA, specialization Mathematical Analysis)
  • Mathematics (programme PřF, N-MA, specialization Mathematical Analysis)
Course objectives
The theory of differential equations ranks among basic parts of mathematical analysis. The course is concentrated especially to linear differential equations with periodic coefficients, some selected parts from the theory of linear second-order equations, solution of differential equations by means of infinite series, generalization of the concept of a solution and to equations with deviating argument.
Syllabus
  • 1. Differential inequalities. 2. Selected parts from the theory of linear differential equations - Floquet theory, linear second-order equations (basic properties, Green function, Sturm comparison theorems, Sturm-Liouville boundary-value problem, oscillation theory). 3. Solution of differential equations by means of infinite series. 4. Generalization of the concept of a solution - Carathéodory solution, existence and uniqueness of Carathéodory solutions. 5. Introduction to the theory of differential equations with deviating argument - basic notions, method of steps, existence and uniqueness for delay equations.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 2nd ed. Brno: Masarykova univerzita, 2001, 207 pp. ISBN 80-210-2589-1. 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
  • 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
  • Hartman, Philip. Ordinary differential equations. New York-London-Sydney: John Wiley & sons, 1964.
  • El'sgol'c, L. E. Vvedenie v teoriju differencial'nych uravnenij s otklonjajuščimsja argumentom. Moskva
  • Driver, Rodney David. Ordinary and delay differential equations. New York-Heidelberg-Berlin: Springer Verlag, 1977.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2000, Autumn 2004, Autumn 2006, Autumn 2008, Spring 2011, Spring 2014, Spring 2016, spring 2018, Spring 2020, Spring 2022, Spring 2024.
  • Enrolment Statistics (Autumn 2002, recent)
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