# Calculator Question: Graphing an Equation for Heat Conduction in a Rod

## Homework Statement

For the rod in Problem 10 (already solved this, see below):
(a) plot u vs. x for t= 5, 10, 20, 40, 100, and 200
(b) plot u vs. t for x= 10, 20, and 30
(c) how long does it take for the entire rod to cool off to a temp. of no more than 1 degree C?

## Homework Equations

u(x,t) = ($\frac{160}{∏^{2}}$)$\sum(\frac{1}{n^{2}})sin(\frac{n∏}{2})sin(\frac{n∏x}{40})e^{(\frac{-n^{2}∏^{2}}{1600}t)}$

## The Attempt at a Solution

I apologize in advance for my barbaric calculator skills.

I plugged the equation above into my TI-89, u(x,t) = y1, as written (including the limits n=1 to ∞). To try to do (a), I simply substituted the numerical values in for the t variable, but receive the "undefined variable" error message when I attempt to graph it. Although I don't have much experience using graphs for series equations, it seems that since the only variable in the y1 equation is x, and the function is supposed to be defined in terms of x, I don't know what the fix is. Would I just be better off going over to the computer lab and trying doing these problems on Maple or something?

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LCKurtz
Homework Helper
Gold Member

## Homework Statement

For the rod in Problem 10 (already solved this, see below):
(a) plot u vs. x for t= 5, 10, 20, 40, 100, and 200
(b) plot u vs. t for x= 10, 20, and 30
(c) how long does it take for the entire rod to cool off to a temp. of no more than 1 degree C?

## Homework Equations

u(x,t) = ($\frac{160}{∏^{2}}$)$\sum(\frac{1}{n^{2}})sin(\frac{n∏}{2})sin(\frac{n∏x}{40})e^{(\frac{-n^{2}∏^{2}}{1600}t)}$

## The Attempt at a Solution

I apologize in advance for my barbaric calculator skills.

I plugged the equation above into my TI-89, u(x,t) = y1, as written (including the limits n=1 to ∞). To try to do (a), I simply substituted the numerical values in for the t variable, but receive the "undefined variable" error message when I attempt to graph it. Although I don't have much experience using graphs for series equations, it seems that since the only variable in the y1 equation is x, and the function is supposed to be defined in terms of x, I don't know what the fix is. Would I just be better off going over to the computer lab and trying doing these problems on Maple or something?
Yes. And you may have to settle for a large upper limit for the sum instead of using ##\infty##.