Ordinary Differential Equations II - NDIR021
Title: Obyčejné diferenciální rovnice II
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
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
Classification: Mathematics > Differential Equations, Potential Theory
Interchangeability : NMMA407
Is incompatible with: NMMA407
Is interchangeable with: NMMA407
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Annotation -
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.
Last update: T_KMA (28.04.2003)
Syllabus -

General existence and uniqueness theorem, dependence on initial conditions and parameters, differential inequalities.

Local behaviour of a solution, equivalence of systems in a neighborhood of a nonstationary point, equivalence of

Orbital stability. Stable and unstable manifold, elementary bifurcations. Boundary value problem for ODE, Green function, Sturm-Liouville problem.

Last update: G_M (04.05.2010)