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...

Extracted text: 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 712, then the temperature u(x, t) in the rod is determined from the boundary-value problem SolUe this B.uP LiT solve B.v.P. l00 (1) k ax 0 <>< l,="" t="">0 at fix) =l0 u(0, t) = 0, u(L, t) = 0, 1>0 (2) u(x, 0) = f(x), 0<>