MA 406
Partial Diff Equations II
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.
Prerequisites: MA222, MA250, either MA306 or MA455.
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.
Prerequisites: MA222, MA250, either MA306 or MA455.
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.
Prerequisites: MA222, MA250, either MA306 or MA455.
