Mathematics 601:

Several quarters of mathematics at the 400-500 level, including Math 568 or its equivalent. Basics of linear algebra such as matrix multiplication, row operations, etc. are assumed.

Math 601; linear 2nd order o.d.e.'s with constant coefficients; being able to recognize (and hence solve) Euler's differential equation.

Some complex analysis, including Cauchy's integral formula; Math 514 would be sufficient.