  A path integral is presented that solves a general class of linear second
order partial differential equations with Dirichlet/Neumann boundary
conditions. Elementary kernels are constructed for both Dirichlet and Neumann
boundary conditions. The general solution can be specialized to solve elliptic,
parabolic, and hyperbolic partial differential equations with boundary
conditions. This extends the well-known path integral solution of the
Schr\"{o}dinger/diffusion equation in unbounded space. The construction is
based on a framework for functional integration introduced by
Cartier/DeWitt-Morette.
