Suppose we wish to find the steady-state temperature u(x, y) in a rectangular plate whose vertical edges x = 0 and x = a are insulated, and whose upper and lower edges y = b and y = 0 are maintained at temperatures f(x) and 0, respectively. See FIGURE 13.5.1. When no heat escapes from the lateral faces of the plate, we solve the following boundary-value problem:
FIGURE 13.5.1 Find the temperature u in a rectangular plate
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u(x, 0) = 0, u(x, b) = f(x), 0 < x < a.(3)
Solution of the BVP
With
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