Solving the heat equation on the real line using fourier transforms

Homework Statement

Solve the heat equation
$\frac{∂}{∂t}$u$(x,t)$=$\frac{1}{α^2}$$\frac{∂^2}{∂t^2]}$u(x,t)

on the real line ℝ with the initial conditions:
u(x,0)= 1 if |x| $\leq$1, 0 for any other value of x

Homework Equations

I don't even know where to start for this question, but I believe that I will have to use a fourier transform, and perhaps separation of variables, to find a solution to this problem

The Attempt at a Solution

I don't even know where to start.

Last edited: