Partial differential equations

This unit covers various analytic methods for partial differential equations.

Explicit solution methods include separation of variables, Fourier series and transforms, fundamental solutions, and more. These methods will be explored for linear and nonlinear equations of elliptic, parabolic, or hyperbolic types.

Abstract analysis techniques will also be covered for some of these partial differential equations, with an emphasis on establishing well-posedness for both stationary and time-dependent partial differential equations, and introducing basic concepts in functional analysis.