Originally Posted by

**Deadstar** Use the formula $\displaystyle u(x,t) = \frac{1}{\sqrt(4 \pi t)} \int^{\infty}_{\infty} e^{-\frac{(x-y)^2}{4t}} f(y) dy$

to find the solution to the heat equation $\displaystyle u_t = u_{xx}$ on the real line with initial condition $\displaystyle u(x,0) = f(x) := e^{-x}$.

My biggest, and maybe only, problem is trying to figure out what to 'do' with the f(y) in the integral, what does it represent?!? As i was typing this though something to do with $\displaystyle f(y) = f(x-t) = e^{-x - t}$ popped into my head however im not sure if this applies to this situation or where i have seen/used it...

Anyone able to give me nudge in the right direction?