Mathematics 210 - Spring term 2005 - Fifth assignment

This assignment requires you to submit spreadsheets concerned with numerical integration. It is due before class time Monday, February 28.
• Question 1. Let N = 20 and use column a to lay out N+1 values of x from 0 to 5. Lay out in column b the corresponding values of f(x) = e-x2 . Then lay out in column c the accumulated areas under the graph of f(x), calculated according to the left rectangle rule. Graph f with an x-y plot and also show the areas under the rectangles with a bar graph, and then graph also the accumulated areas.

Save as m210.5.1.ms.

• Question 2. Do the same calculations, but forget the graphs, with N=40, 80, all the way to 1280. Store the total areas under the graph in a separate column each time you calculate it. Make a bar graph showing these areas (one bar for 40, etc.)

Save as m210.5.2.ms.

• Question 3. In another column, calculate the estimates you get of areas by Richardson extrapolation. Plot these in a bar graph allowing them to be compared to the previous ones.

Save as m210.5.3.ms.

• Question 4. Plot 32 values of x from 0 to 5, then the same f(x) as before, then plot the area from 0 to x as a function of x by using the trapezoid rule.

Save as m210.5.4a.ms.

Do the same with 64 values. Save as m210.5.4b.ms.

• Question 5. Finally do the same using 64 intervals and Simpson's rule. Comment on how accurate the value you get for the total area is (this will involve some real work).

Save as m210.5.5.ms.

If you find these questions confusing, please write me.