Homework 9  427K-H     Due Monday April 23



1. page 528 #17  a), b).


2. Page 528 # 17  c), d).


3. Find the first few terms of the solution of Bessel's equation


     y" + (n-1)(1/x) y'  +  y  =  0.


 Assume that  y(0) =1  and y'(0) = 0.

Now find the iterative equation for the m-th term in the series.


4. Problem 28, page 267  (see also problem 22,29 for your information.)

The Legendre equation comes from the Laplace operator in three dimensions.
It is (1-x^2) y" - 2 x y' + r(r+1)y = 0.  (My r is the book's /alpha).
Problem 28 asks that you show that two solutions of Legendre's equation
for different r, which are bounded on the interval [-1,1], are orthogonal.
We should be talking about orthogonality Friday in class.


5.Find the Fourier series of the function  f(x) = x^2  on the interval
[-1,1].



Extra Credit:

Page 267 # 26 (see the note before # 22).

Page 515 #27, b,c) (Everybody needs to see an elliptic integral).