Math 230 - Chapter 6 Study Guide

1. Rewrite a linear combination of power series into a single power series.
2. Without solving the differential equation, find a lower bound for the radius of convergence about two ordinary points.
3. Given the equation involving constants that results after substituting the power series into a differential equation, find two solutions.
4. Determine the singular points and classify them as regular or irregular.
5. Find the indicial roots and determine whether or not they differ by an integer.
6. Find the solution to the Bessel's equation.
7. Find the Legendre's Polynomials using Rodrigues' method.
8. Solve the Legendre's equation.
9. Find two power series solutions about the ordinary point.
10. Find two linearly independent power series solutions using the method of Frobenius.

Notes

• This is a take home exam.
• After setting up the problems, you should use the computer as much as possible to solve them.
• The makelist command in Maxima will be extremely helpful for questions 3, 7, 9, and 10.

Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 4 4 6 4 4 9 3 4 6 6 50