Credits: 7.5

Type: bridging

Objectives:

• To understand the basic results of the theory of ordinary differential equations
• To understand the aspects of qualitative theory that make useful descriptions of phase space possible.

Knowledge:

• Aspects of basic theory (regularity of solutions, etc).
• Elementary methods of numerical solution.
• Flows (conjugation, conjugation of linear systems, Hartman's theorem, invariant varieties, application of Poincaré).
• Stability.
• Poincaré-Bendixson's theorem.
• Introduction to perturbation theory.

Subject-specific competences:

• To be able to obtain information about solutions based on qualitative and numerical results.
• To be able to draw phase portraits of a Poincaré application.
• To determine solution stability.
• To identify both the alpha and omega limits of smooth fields.
• To analyse properties and approximate solutions of systems close to systems with known solutions.