Homework assigned 10/7, due 10/16

Section 5.5

Written problems: 1, 2b, 5, 7, 10, 13, 15a
Computer problems: 1, 2, 4. For all three of these problems, compare the results against Simpson's rule where Simpson's rule is done on a uniform mesh, with 10, 100, and 1000 mesh-points. (Present all three values from the Simpson's rule in addition to the value from the Guassian quadrature.)

Another Computer Problem

Compare the Gaussian quadrature method for n=4 (see table 5.1) against Simpson's method to find the integral of sin(x) from -1 to 1. How small does h have to be for Simpson's method to be as accurate as the Gaussian Quadrature method? Repeat this problem for the integral of cos(x) from 0 to 10.