Mathematics 210  Spring term 2003  eighth assignment
This assignment requires you to submit several spreadsheets concerned
with solving differential equations and doing matrix manipulations.
This lab and the redone midterms are due Wednesday, March 19,
by class time.
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.
The graph signature
mechanism should now be working  please use this feature.

Question 1.
Use Euler's method to solve
x'(t) = 2 y(t)
y'(t) = x(t)  3y(t)
in the range t=0 to 10.
Use initial conditions
(1,0),
(0,1),
(1,0),
(0,1)
all on one sheet.
Use a step size of 0.1.
Graph the parametrized curves (x, y).
Save this sheet as m210.8.1.ms.

Question 2.
Use Improved Euler's method to answer the same question.
This question will require a ridiculous number of columns if you do
the obvious thing. After you have made a good plot,
"Edit/Convert" the (x,y) data to
fixed numbers
and move them somewhere else.
Then rebuild the part of the "live" area that you converted.
Save this sheet as m210.8.2.ms.

Question 3.
Find e^{A dt} where dt = 0.1,
correct to about 8 significant figures.
Do this by summing the Taylor's series to enough terms.
Use this calculation to make the same graphs as in the earlier questions.
Save this sheet as m210.8.3.ms.

Question 4.
Do the last question,
but for the system
x' = x  y
y' = x  y
Save this sheet as m210.8.4.ms.
That's it!
If you find these questions confusing, please
write me.
