Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Ordinary Differential Equations I - NDIR020

Title:	Obyčejné diferenciální rovnice I
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer 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

Classification:	Mathematics > Differential Equations, Potential Theory
Incompatibility :	NMMA333
Interchangeability :	NMMA333
Is incompatible with:	NMMA336, NMMA333
Is interchangeable with:	NMMA336, NMMA333

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: T_KMA (28.04.2003)

Existence and unicity theorems, global existence, continuous and differentiable dependence on initial conditions and parameters, linear systems and linear equations of the n-th order. Autonomous equations, dynamical systems. Periodic and bounded solutions of linear systems, Floquet theory. Lyapunov stability, linearization theorems, Lyapunov functions, La Salle principle. Topological equivalence of linear systems; Hartman-Grobman theorem; stable, unstable, central manifolds. Bifurcation from the equilibrium, normal forms. Boundary value problems for the second order linear equations.

Syllabus -

Last update: G_M (04.05.2010)

Solution of a differential equation, existence, uniqueness, elementary methods of integration.

Maximal solutions, global existence, Gronwall lemma.

Linear systems and linear equations of n-th order, existence, uniqueness, fundamental system, variation of constants. Constant coefficients.

Types of stability, Ljapunov function, orbital stability.

Elementary bifurcations. Poincare-Bendixson theory.

Controllability and stabilizability of linear systems by feedback, quadratic optimal control problem for linear systems.