Mathematics 210 - Spring term 2003 - Second assignment

This assignment requires you to submit several spreadsheets concerned with high order approximations and more numerical integration. It is due by 11:00 AM Friday, January 24.

Postponed to Monday because of spreadsheet problems with #1

I repeat the instructions from the first lab:

  • Go to the MathSheet home page and then to the applet page. Open a running copy of the spreadsheet and return to this page.
  • Log in immediately: File/Log in. Your login id is your Mathematics Department login name, and your password is your student number. This allows you to save and load spreadsheet files. You should save your work frequently.
  • Question 1. In the first column lay out values from -6 to 6 in 256 steps. In the second column lay out values of cos x over the same range. Make a graph of this function. Make the x and y scales the same. Then lay out a column containing the values of the first 7 coefficients of the Taylor series of cos x at x = /4. Then make up columns of the first 7 approximations to cos x (0th order, 1st order etc. through 6th order), but including only values small enough to be seen on your graph. I.e. do not attempt to calculate the values when they are large. Put these graphs in different colours and label them. (Labels and graphs in same colour. That could be as many as 7 different polynomial graphs. Keep in mind that each XY plot needs two columns of data to work with. There are no shortcuts.) Save this sheet as

  • Question 2. Use Simpson's rule to get an estimate accurate to 16 decimal places with the minimum number of values calculated of the integral from 0 to 6 of e-x2. Hint: Simpson's rule adds together terms (h/6)(f(a) + 4f(a+h/2)+ f(a+h)). The values at the odd points - the mid-points - have to be treated differently from the others. Put the even ones in column a and the odd ones in column b. Graph the function and its integral as function of x. Save this sheet as

  • Question 3. Use Simpson's rule with an interval of 1/2 to calculate the integral of cos x2 over the range 0 to 1. Do the same with interval of 1/4. Use just these data to estimate the error in the first, then to make the best estimate you can. Save this sheet as

  • Question 4. Use Simpson's rule with an interval of 0.1 to calculate the integral of cos x2, but over the range 0 to 10. Plot the function and the integral on a graph. Save this sheet as
That's it!

If you find these questions confusing, please write me.