Ordinary Differential Equations

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

The course is a continuation of Mathematics III or any undergraduate one-semester course in ordinary differential equations. It provides, in a greater depth, a review of concepts and techniques for solving first order equations. Then autonomous systems, geometric aspects of the two-dimensional phase space and stability of solutions are among the main topics studied.

Requirements:

Syllabus of lectures:

1-2. Survey of solution methods for ordinary differential equations of the first order. Geometrical meaning of a differential equation. Equations in differentials.

3-4. Autonomous systems. Explosion of solutions (blow-up). Global solutions. The method of apriori estimates.

5-6. Dynamical systems. Semigroups. Basic notions and properties.

7-8. Partial differential equations of the first order (optional).

9-10. Hamiltonian systems and systems with a damping. Conservative, dissipative systems.

11-12. Stability of linear and nonlinear systems. Tests for obtaining stability. Atractors.

13-14. Stability and linearization. Stability and Lyapunov functions.

Syllabus of tutorials:

1-2. Survey of solution methods for ordinary differential equations of the first order. Geometrical meaning of a differential equation. Equations in differentials.

3-4. Autonomous systems. Explosion of solutions (blow-up). Global solutions. The method of apriori estimates.

5-6. Dynamical systems. Semigroups. Basic notions and properties.

7-8. Partial differential equations of the first order (optional).

9-10. Hamiltonian systems and systems with a damping. Conservative, dissipative systems.

11-12. Stability of linear and nonlinear systems. Tests for obtaining stability. Atractors.

13-14. Stability and linearization. Stability and Lyapunov functions.

Study Objective:

Study materials:

[1] Stanley J. Farlow: An introduction to differential equations and their applications. McGraw-Hill, Inc., New York 1994. ISBN 0-07-020030-0.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: