This learning unit (LU) aims at providing knowledge and competencies about the principles, concepts, and techniques of Ordinary Differential Equations, with emphasis in qualitative theory aspects (conjugacies, stability, bifurcations, etc.).
Ordinary Differential Equations Qualitative Theory
Upon conclusion of this LU the student should:
- know the methods studies, the main theorems and their;
- have acquired enough familiarity with the kind of arguments and techniques used in the examples studied, so that, afterwards, he/she can both apply them to different contexts, and proceed to produce original research studies in these matters.
1) Existence of solutions; uniqueness; non-existence
2) Continuation of solutions; dependence on initial conditions and parameters
3) Basic notions of phase portraits
4) Linear ordinary differential equations
5) Staility and Lyapunov functions
6) Hyperbolicity, conjugacies, linearization
7) Planar systems: Poincaré-Bendixon theory
8) Introduction to bifurcations, centre manifolds, and normal forms
Barreira & Valls: Equações Diferenciais: Teoria Qualitativa, IST Press, 2010;
Chicone, Ordinary Differential Equations with Applications, 2nd Ed., Springer, 2006;
Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.