This topic includes: First and second order differential equations in the phase plane. Linear approximations at equilibrium points. Index of a point; limit cycles; averaging, regular and singular perturbation methods. Stability and Liapunov's method. Bifurcation. Basic ideas of calculus of variations. The Euler-Lagrange equations; eigenvalue problems. Applications to second and higher order differential and partial differential equations. Rayleigh-Ritz and Galerkin methods and discrete models.
This topic aims to: