Mathematics 371 – Numerical Analysis Problem Set 3 October 10, 2001

From the text:

• Section 3.1: 1a,c, 3a,c, 3a, 7a, 10, 17, 25, 29. However, change the directions for problem 25 as follows: Instead of using the Lagrange form of the interpolating polynomial by hand, use the following Maple commands to do this problem. Begin by loading the CurveFitting package with:

                            with(CurveFitting);

The command we want in this package is called PolynomialInterpolation (note the capitalization – you will need to enter it exactly like this). This function will compute the interpolating of degree ≤ n for a list of n + 1 points. To use it, you can begin by creating a list of the x-values you want, for instance:

                       xlist := [0.2,0.35,0.4,0.55];

Then do the same for the y- or f(x)-values you want. These should be listed in the same order as the x-values.

                      ylist := [12.3,13.3,14.5,17.9];

Then the command

               IP := PolynomialInterpolation(xlist,ylist,x);

will compute the interpolating polynomial as a function of the variable x, and assign it to the variable IP. You can then perform any other computations you want with this (plotting, differentiating, root-finding, etc.) Do parts a and b of the problem from the text. Then add the following part:

c) Plot your interpolating polynomials to visualize where the maxima are located. Do you think these interpolating polynomials approximate the true weight curves very well? Explain.

• Section 3.2/1a, 2a, 5a, 7, 14, 17. Assignment

Individual writeups due Wednesday, October 17.