Independently reproduce the results of the example of this section.

The results for this exercise are provided already in the text. Your task is to reproduce them independently. This will be easiest with some analytic software package such as Mathematica or MatLab. However, the results can be reproduced using just a spreadsheet. The first (and most significant) task is to construct a spreadsheet that evaluates [3.213] using the trapezoidal rule, [3.218] and approximation [3.219]. With this, you can evaluate [3.213] at y^[1] = 0.000 and y^[2] = 1.000. This will give you the results of the first two rows of Table 3.31. Confirm that you obtain the same values as indicated in the table. Next, based upon those values, apply the secant method [3.220] to obtain a value for y^[3], which should be –4.207. Apply your spreadsheet implementation of the trapezoidal rule to this to complete the third row of Table 3.31. Again, confirm you have obtained the same value as indicated in the table. Apply the secant method again, and continue in this manner until you have reproduced all the results of Table 3.31.