Goal: To provide an overview of the fundamental concepts of one and two-dimensional
dynamical systems. Moreover, the course discusses the methods of calculus of variations with
applications in mechanics, and elements of PDEs (heat and wave equations in Euclidean
spaces)
Course description: Dynamics of first and second order differential equations, stability of fixed
points through linearization. Energy methods and Lyapunov direct methods. Periodic solutions,
limit cycles. Calculus of variations. Hamiltonian and Lagrangian systems, Legendre transform.
Elements of PDEs: method of characteristics, heat equation, wave equation.
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