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:
  • 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

  • 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

  • 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

  • Question 4. Do the last question, but for the system

    x' = -x - y
    y' = x - y

    Save this sheet as

That's it!

If you find these questions confusing, please write me.