Mathematics 5101:

Several quarters of mathematics at the 21xx-4xxx level, including Math 2568 or its equivalent. Basics of linear algebra such as matrix multiplication, row operations, etc. are assumed.
Mathematics 5102:
Math 5101; 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 4552 would be sufficient.