Ordinary Differential Equations I - NDIR020
Title: Obyčejné diferenciální rovnice I
Form of teaching: lecture+practicals
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Duration in semesters: 1
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Maximum number of enrolled students: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Repeated enrollment: 2 / 2 / 2 / 2
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 -
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 -

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.

Last update: G_M (04.05.2010)