Homework #3
Instructions. This is due on February 16 at the beginning of
class. It is worth 20 points. Late papers lose 3 points per day late. You must
work by yourself, but feel free to consult with me. Explain what you did and
why you did it: good explanations are essential! Your paper should have an
introduction, a main body and a conclusion. Start early, ask questions and do
well.
Introduction. In this assignment, you
will use the ODE Architect software that came with the book. Let me know quickly
if you have any trouble installing or using this software.
Problems. Start by running “Multimedia ODE Architect” and choosing “Cool First
Order ODEs” and then “Cooling an Egg.” The opening
screen has a demonstration with narration. Watch it as long as you want, click
the right arrow in the lower right corner of the screen when you’re ready to
move on.
On the new screen, you are asked to enter the
right-hand side of the equation for the cooling egg based on the word
description given. (Type in Te and Tout for the terms.
You will need to use * for multiplication.) After typing your answer, hit Enter
and see if you’re right. Change your response if you need to. When you have the
correct answer, explain in one sentence why the equation matches the word description
given; pay special attention to + and - signs. Then, with Tout
= 68, click Solve and briefly explain what is happening to the solution. Change
Tout to Tout = 212, click Solve and briefly explain what
is happening to the solution. Why does this solution look different? When you
have these questions answered, click the right arrow to go to the next page.
Start on this new page by clicking Solve to draw a
solution curve. Then increase the value of k by several points and click
Solve again. Describe the difference in the two solutions, and use the
difference to explain what the effect of k is (in particular, what
happens if k increases and what happens if k decreases). Explain
what changes if Tout is increased (do an experiment if you need to).
Explain what changes if Te is increased (again, do an experiment if
you need to). When you have these questions answered, click the right arrow to
go to the next page.
On this page, data is shown from “real” measurements
of a cooling egg. Click on Solve to see a solution curve for the given values
of k and Te(0). List several ways in
which the solution curve is inadequate as a match to the data. Based on this
graph, to get a good match should you increase or decrease Te(0)? Briefly explain. Based
on this graph, should you increase or decrease k? Briefly explain. Make
your best guesses as to how much to change each parameter (write this down),
and try Solve again. Discuss how well this graph fits the data. Indicate how
you think each parameter should be changed to do even better. Continue to
adjust Te(0) and k (you do not
need to provide details) until you have the “best” fit you can get (it won’t be
perfect). Write down the values of Te(0)
and k and briefly discuss any problems with the fit. Even your best
graph won’t be perfect; if you had to guess, which temperature measurement is
most likely to be inaccurate?
You’re done! Click the right arrow, then Exit, then
Quit Program, then Yes.