## 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 re-done mid-terms are due Wednesday, March 19, by class time. I repeat the instructions from the first lab:
• 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 eA 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.