(Same as Electrical and Computer Engineering M208B.) Lecture, four hours. Requisites: courses 115A and 115B (or Electrical and Computer Engineering 208A), 131A, 131B, 132. Topics may include L^{p} spaces, Hilbert, Banach, and separable spaces; Fourier transforms; linear functionals. Riesz representation theory, linear operators and their adjoints; self-adjoint and compact operators. Spectral theory. Differential operators such as Laplacian and eigenvalue problems. Resolvent distributions and Green's functions. Semigroups. Applications. S/U or letter grading.