  Let $u_t-a(t)u_{xx}=f(x, t)$ in $0\leq x \leq \pi,\,\,t\geq 0.$ Assume that
$u(0,t)=u_1(t)$, $u(\pi,t)=u_2(t)$, $u(x,0)=h(x)$, and the extra data
$u_x(0,t)=g(t)$ are known. The inverse problem is: {\it
  How does one determine the unknown $a(t)$?}
  The function $a(t)>a_0>0$ is assumed continuous and bounded. This question is
answered and a method for recovery of $a(t)$ is proposed. There are several
papers in which sufficient conditions are given for the uniqueness and
existence of $a(t)$, but apparently there was no method proposed for
calculating of $a$. The method given in this paper for proving the uniqueness
and existence of the solution to inverse problem is new and it allows one to
calculate the unknown coefficient $a(t)$.
