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Ordinary Differential Equations in Real Domain - NDIR012

Title:	Obyčejné diferenciální rovnice v reálném oboru
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Josef Kofroň, CSc.
Classification:	Mathematics > Differential Equations, Potential Theory
Incompatibility :	NMMA333
Interchangeability :	NMMA333
Is incompatible with:	NMMA336, NMMA333
Is interchangeable with:	NMMA336, NMMA333

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Annotation -

Last update: T_KNM (18.05.2008)

Study of systems of linear and nonlinear ordinary differential equations of the first order.

Aim of the course -

Last update: T_KNM (18.05.2008)

Fundamentals of the theory of ordinary differential equations.

Literature - Czech

Last update: T_KNM (18.05.2008)

Kofroň J.: Obyčejné diferenciální rovnice v reálném oboru, Karolinum, 2004

Kurzweil J.: Obyčejné diferenciální rovnice, SNTL, 1978

Teaching methods -

Last update: T_KNM (18.05.2008)

Lectures and seminars in the classroom.

Requirements to the exam -

Last update: T_KNM (18.05.2008)

Examination according to the syllabus.

Syllabus -

Last update: T_KNM (18.05.2008)

Systems of differential equations of the first order, conversion of one equation of the nth-order to the system of the first-order equations, a matrix form of a system of equations. The definition of the solution, field of directions, equivalence of a differential equation and a corresponding integral equation.

Cauchy problem for the system of linear equations of the first order, Gronwall inequality and its alternated versions. Existence and uniqueness of the solution for a continuous right-hand side. Fundamental matrix, the Liouville theorem, the formula for variation of constants.

Systems of linear differential equations with constant coefficients, the case of distinct and multiply nodes, stability of the solution, a generalized exponential function.

Systems of nonlinear differential equations of the first order by the assumption of the continuity of the right-hand side, existence and uniqueness of the solution - Lipschitz condition,local and global properties. The relation of the graph of the solution and a compact subset of the definition domain of the right-hand side of the equation. The Kneser theorem, the Fukuhara property. The continuity property of the solution on initially conditions and parameters. The differentiability of the solution on initially conditions and parameters, variational equations.

The properties of solutions of autonomous equations.

Carathéodory theory of linear and nonlinear systems of differential equations of the first order.

Entry requirements -

Last update: T_KNM (18.05.2008)

There are no special entry requirements.