Analytic ordinary differential equations: series solutions of ordinary differential equations about ordinary and regular singular points. Asymptotic solutions. Sturm-Liouville theory. Bessel and Legendre functions. Fourier series. Precludes additional credit for MATH 3404 and PHYS 3808. Prerequisite(s): MATH 2000; and MATH 2454.Lectures three hours a week and one hour tutorial.