Fourier transform for the heat problems Solving the heat problems l(x,)→>U/(k,t) 4-aZ=0 q(x)→>d(k) U+aku=0 Ulo=Φ 1=0 u=U(k, t)e dk u=vs)ds expl 4at U=dexp(-k'a'tFourier Transform for the heat problems     =  + = =0 2 2 | 0 t t U U a k U a t u s ds a t x s   2 exp[ ] ( ) 2 2 4 ( − ) − =  Solving the heat problems     = − = = | ( ) 0 0 2 u x u a u t t xx  exp( ) 2 2 U =  −k a t ( ) ( ) ( , ) ( , ) x k u x t U k t →  →   u = U k t e dk ikx ( , )