Ordinary linear differential equations: existence and uniqueness theorems (no proofs), Wronskians; solution in series for first and second order non-singular and regular singular equations; methods of Frobenius.
Fourier series: two-dimensional separable linear partial differential equations; solutions by separation of variables and Fourier series.
Functions of a single complex variable: continuity, differentiability, Cauchy-Riemann equations; analyticity, power series; Cauchy's Theorem and applications to evaluation of integrals.