The following functions are used to determine the temperature distribution in a

@n=7 change is .004% @n=9 change

ID: 3553632 • Letter: T

Question

The following functions are used to determine the temperature distribution in

a flat square metal plate where the temperature is held constant at T1 on three sides, and T2

on the fourth side:

(This expression indicates that the term following the summation sign %uF053 is two be

computed for all odd values of m <= n, and these values are to be added together.)

Suppose x =1 ft, y = 1 ft, T1

= 70o F, T2

= 200o F, and the length of a side L = 2 ft. You need

to determine how large the value for n in the second expression for w(x, y) has to be in

order to %u201Cclosely%u201D approximate the first expression. Specifically, how large does the value

for n have to be so that the addition of the next term in the series (m = n + 2) produces a

change in T of less than .001%.

The entry in your answer file for this question should have the form:

% Problem 4:

% n_min = some odd integer

@n=7 change is .004% @n=9 change <0.001%

so n=7

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