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3. Let u(x, t) denote temperatures in a slab 0

3. Let u(x, t) denote temperatures in a slab 0 <x < 1 that is initially at temperature zero throughout and whose faces are at temperatures u(0,1) 0 and u( )F(), where F() and F() are continuous when t 0 and where F(0) 0. The unit of time is chosen so that the one-dimensional heat equation has the form u,(x,1) = uxx(x, ). Write n(x, t) = U(x, t) + xF(t), and observe how it follows from the stated conditions on the faces of the slab that U(0,1)-0 and U(1,1)=0. Transform the remaining conditions on u(x, t) into conditions on U(x, t), and then refer to the solution found in Problem 1 to show that 2 (1 n n-1 4. Show that when F(1) = A1, where A is a constant, the expression for u(x, t) derived in Problem 3 becomes sin nTx 

3. Let u(x, t) denote temperatures in a slab 0

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