Math 224--Differential Equations: Project 2, Spring 1997

the Prevailing Weather...

by Gavin LaRose (glarose@umich.edu), Nebraska Wesleyan University, January 1997

permission granted to use and distribute free in an academic setting

After your resounding initial success, RiMaC is making strides in becoming a recognized mathematical consulting company not only in the Lonlinc area, but also on the West coast---as evidenced by the latest contract, from the prestigious Dran Corporation think-tank, based in sunny Gos Andies, Ifcal.

DVI file of project
PostScript version of project

The letter...

Dran Corp

1 Dran Rd.
Gos Andies, IF
80999

7 March 1997

Rigorous Mathematical Contractors (RiMaC), Inc.
Lonlinc, SK 04685

Dear RiMaC:

On the recommendation of EcoSystems, Inc., we are contacting you with a matter which, though not concerned with fish, is certainly, in some senses, fishy. As you undoubtly know, we are at Dran concerned with all manner of investigations which are commissioned by other interests---much as is your company. One such concerns the nature of of global warming, a project on which we have been working periodically subject to the availability of funding from the interested group(s). The primary work in the area was completed under the auspices if an initial grant, which expired some time ago before the project was brought to a close. We have recently been contacted by the funding agency with news that additional funding has been procured, but in the interim, to our great annoyance, the brilliant mathematician we initially had working on the matter has eloped with the previous CEO of Dran Corp. We are therefore subcontracting the matter with an outside source, namely your company.

The records we have of the model proposed by the previous researcher indicate that the deviation, w, from the global average temperature (which deviation is induced primarily by the introduction of pollutants into the environment) is governed by the equation

w''(t) = -b w(t) - a w'(t) + c w(t)2 (1 - w(t)).
Here t is given in decades measured from the present, b is a measure of the resiliancy of the global environment, which acts to counter change, a represents environmental `friction' opposing change, and c is an indicator of the amount of pollution being produced by the industrialized countries of the world. In the margin of the record in which this model is found, the previous researcher has written ``thus substantial change in the global climate is possible, though this margin is too small to demonstrate this.''

There being no work to substantiate this bold assertion, we need you to determine whether it is in fact correct. Given what we are modeling, it is clear that the exact values of the parameters a, b, and c are not precisely known, nor is the degree to which the current global temperature is elevated. However, the nature of the model suggests that a and b should be between 0.5 and 1.5 and the estimates of global warming point to a temperature increase on the order of 1oC. The most variable parameter is that measuring pollution, c, which (depending on the success of international pollution reduction efforts) could be several times as large as the other parameters in the problem.

As is our custom, we have established a liason in the local scientific community whom you should contact with any questions you may have in completing this project. This is the enthusiastic Dr. Gavin LaRose, who begged to be allowed to complete the project on his own. Unfortunately, his fee was too high and we have therefore retained him only as a consultant. You should be in touch with him by the 13th and 20th of March with an indication of your progress, and your final 3--5 page typewritten report is due by the 11th of April.

Sincerely,
W. R. N. Cristof'r
Consultant-in-Chief, Dran Corp.

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