Goal: To provide an overview of the fundamental concepts of planar dynamical systems. Moreover, the course discuss 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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