Followed by Solving initial value problem for wave equation via Fourier transform, in this topic I will show you how to solve initial value problem for heat equation via Fourier transform.

Following is the problem

From the equation by taking Fourier transform to the both sides, we obtain

.

This is an ODE, the solution is given by

.

From the initial date we get

which implies that

.

Thus, we obtain

.

Finally, we obtain by taking the inverse Fourier transform

.