Mathematics 210 - Spring term 2003 - seventh assignment
This assignment requires you to submit several spreadsheets concerned
with solving differential equations.
This lab and the re-done mid-terms are due Wednesday, March 19,
by class time.
I repeat the instructions from the first lab:
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Go to the MathSheet home page
and then to the applet page. Open a running
copy of the spreadsheet and return to this page.
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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.
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Question 1.
Use the spread sheet to solve the differential equation
dy/dt = -y + cos(2t) and initial condition y(0) = 1
with step size dx = 0.1
for the range t=0 to 20. Do this by each of the three methods
explained in class: Euler's, Improved Euler's, Runge-Kutta of order 4.
Do all of these on one sheet. Graph the solutions you get.
Save this sheet as m210.7.1.ms.
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Question 2.
Use the spread sheet to solve the differential equation
dy/dt = -y + t and initial condition y(0) = 1.
Use Improved Euler over the range 0 to 6.
Find roughly the largest step size you can that will give you an answer at the end
correct to 4 decimals.
Graph your solution.
Save this sheet as m210.7.2.ms.
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Question 3.
An object at the surface of the Earth accelerates
at 9.8 m/s2. The radius of the Earth is
6370 kilometers. If you drop an object
from rest at a distance of 10,000 kilometers from
the centre of the Earth,
how long does it take for it to hit the Earth?
Answer correct to 1%. Ignore air friction.
Explain your accuracy.
Save this sheet as m210.7.3.ms.
That's it!
If you find these questions confusing, please
write me.
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