13.3 Heat Equation
INTRODUCTION
Consider a thin rod of length L with an initial temperature f(x) throughout and whose ends are held at temperature zero for all time t > 0. If the rod shown in FIGURE 13.3.1 satisfies the assumptions given on page 721, then the temperature u(x, t) in the rod is determined from the boundary-value problem
![A thin finite rod of length L coincides with the x axis on the interval [0, L]. The cross section area at the beginning of the rod is indicated by an arrow and labeled u = 0. The cross section area in the middle of the rod is indicated by an arrow and labeled u(x, t). The cross section area at the end of the rod is indicated by an arrow and labeled u = 0.](/api/v2/epubs/9781284206258/files/images/ch13-9781284207972_CH13_FIGF0301.png)
FIGURE 13.3.1 Find the temperature u in a finite rod
(1)
(2)
(3)
In the discussion that follows next we ...
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