Topics include basic normed linear space theory; fixed-point theorems and applications to differential and integral equations; Hilbert spaces and the spectral theorem; applications to Sturm-Liouville problems; approximation and computational methods such as the Galerkin, Rayleigh-Ritz, and Newton procedures. Computational Science, Engineering, and Mathematics 386C and Mathematics 383C may not both be counted. Three lecture hours a week for one semester.