Ordinary Differential Equations II.

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

An advanced course of qualitative theory of ordinary differential equations.

Requirements:

Syllabus of lectures:

Exponentials of linear operator. Exponential matrix. The flow defined by a linear differential equation. Invariant subspaces of state space. Stability theory of linear systems. Hurwitz?s criterion. Laplace transform-applications in dynamics. Autonomous nonlinear systems. Existence-uniqueness theorem. The flow defined by nonlinear differential equation. Invariant manifolds in state space. Stability of hyperbolic equilibrium points. The Hartman-Grobman theorem. Stability of nonhyperbolic equilibrium points-Liapunov function. Hamiltonian and Newtonian systems.

Syllabus of tutorials:

Exponentials of linear operator. Exponential matrix. The flow defined by a linear differential equation. Invariant subspaces of state space. Stability theory of linear systems. Hurwitz?s criterion. Laplace transform-applications in dynamics. Autonomous nonlinear systems. Existence-uniqueness theorem. The flow defined by nonlinear differential equation. Invariant manifolds in state space. Stability of hyperbolic equilibrium points. The Hartman-Grobman theorem. Stability of nonhyperbolic equilibrium points-Liapunov function. Hamiltonian and Newtonian systems.

Study Objective:

Study materials:

[1] Perko L., Differential equations and dynamical systems, 1998, ISBN 0-387-94778-7

[2] Lynch S., Dynamical systems with applications using MAPLE, 2001, ISBN 0-8176?4150-5

[3] Čipera S., Diferenciální rovnice a dynamické systémy, 2006, ISBN80-01-03451-8

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: