Ma 404: Numerical Methods Reading and Homework Assignment 6 Prof. Wickerhauser Read Chapter 5, Sections 5.1 to 5.5, of the text. Do Exercise 2(b) of Section 5.1, pp.259--261. Do Exercise 5 of Section 5.1, pp.259--261. Do Exercise 6 of Section 5.1, pp.259--261. Do Algorithm 4(a,b,c) of Section 5.1, p.262. Do Exercise 2(c) of Section 5.2, pp.275--277. Do Exercise 12 of Section 5.2, pp.275--277. Do Exercise 2(a,b) of Section 5.3, p.294. Do Exercise 2 of Section 5.4, p.307. Do Exercise 7 of Section 5.4, p.307. Do Exercise 8 of Section 5.5, p.319. Do Algorithm 1 of Section 5.5, p.319. For the next two problems, set cas(x)= cos(2*PI*x)+sin(2*PI*x). Problem H06.1. Fix N and show that, if n and m are in the range [0,1,...,N-1] with n not equal to m, then the sum from k=0 to k=N-1 of cas(n*k/N)*cas(m*k/N) equals 0. What is the value when n=m? Problem H06.2. Show that, for N=2M and any function f=f(k) defined on 0,1,...,N-1, we have that the sum from k=0 to k=N-1 of f(k)*cas(n*k/N) equals the sum from k=0 to k=M-1 of f(2*k)*cas(n*k/M) plus the sum from k=0 to k=M-1 of f(2*k+1)*cas(n*k/M + n/2M).