Ordinary Differential Equations

Existence And Uniqueness Theorem. Differentiable Dependence On Initial Conditions.Linear Equations. Exponential Of Matrices. Classification Of Linear Fields. Canonical Jordan Form. Non-Autonomous Linear Equations: Fundamental Solution And Liouville’s Theorem. Non-Homogenous Linear Equations. Periodic Coefficients Equations, Floquet’s Theory. Asymptotic Stability And Instability Of A Singular Point Of An Autonomous Equation. Lyapounov Functions. Fixed Hyperbolic Points. Statement Of The Grobman-Hartman Linearization Theorem. Associated Flow To An Autonomous Equation. Limit Sets. Gradient Fields. Hamiltonian Fields. Vector Fields In The Plane: Periodic Orbits And The Poincaré-Bendixon Theory. Hyperbolic Periodic Orbits. Van Der Pol’s Equation.

Referências:
ARNOLD, V. – Equations Differentialles Ordinaires. Moscou, Ed. Mir, 1974.
HIRSCH, M. e SMALE, S. – Differential Equations, Dynamical Systems and Linear Algebra. New York, Academic Press, 1974.
PONTRYAGIN, L. S. – Ordinary Differential Equations. Reading, Mass., Addison-Wesley, 1969.
SOTOMAYOR, J. – Lições de Equações Diferenciais Ordinárias. Rio de Janeiro, IMPA, Projeto Euclides, 1979.

 

* Standard program. The teacher has the autonomy to make any changes.