Normal variables. The relation of transverse and longitudinal fields to device design. Hilbert spaces and the meaning of bra-ket notation. Comparison of finite dimensional vector spaces and infinite dimensional function spaces. Deriving the Green function and its local density of states. Basic consequences of scattering theory. Singular value decomposition and modal descriptions. Krylov solvers. Volume integral equations. Device design and optimization theory. Computational and physical approximations of wave equations.