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 m210.2.1.ms.

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 midpoints 
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 m210.2.2.ms.

Question 3.
Use Simpson's rule with an interval of 1/2
to calculate the integral
of cos x^{2} 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 m210.2.3.ms.

Question 4.
Use Simpson's rule with an interval of 0.1
to calculate the integral
of cos x^{2}, but over
the range 0 to 10.
Plot the function and the integral on a graph.
Save this sheet as m210.2.4.ms.
That's it!
If you find these questions confusing, please
write me.
