MA 406

Canonical forms of linear second order PDEs. Ill-posed and well-posed problems. General framework for linear PDEs: self-adjoint and positive definite linear operators, minimization principle, Rayleigh quotient, Eigenfunction series. Green’s functions in the planar case; deltafunction in higher dimensions. Introduction to numerical methods for PDEs. Additional topics may include weak solutions, linear and nonlinear evolution equations, linearization and stability, heat and forced heat equations, maximum principle, nonlinear diffusion, and dispersion and solitons. <br>