Important Prerequisites for Math 603.02:

1. By the second week:
    Know how to solve (a) a second order ordinary differential equation with constant coefficients,
                                   (b) Euler's homogeneous differential equation.

2. By the third week:
    Know (a) the CAUCHY-GOURSAT integral theorem,  
               (b) the RESIDUE of a complex function at a singularity,
               (c) CAUCHY'S INTEGRAL FORMULA

    Look them up in a text on complex variables.
    R.V. Churchill's "Complex Analysis and Aplications" is a good possibility.

3. By the fifth week:
    Know the "Basic Properties of a Sturm-Liouville Eigenvalue Problem" (Section 3.3.3 in "Linear Mathematics in Infinite Dimensions").
    In particular, you should know how to use Exercise 3.3.4 ("How to normalize an eigenfunction")