1. The problem statement, all variables and given/known data Show that if v(x,t) and w(y,t) are solutions of the 1-dimensional heat equation (v_t = k*v_xx and w_t = k*w_yy), then u(x,y,t) = v(x,t)w(y,t) satisfies the 2-dimensional heat equation. Can you generalize to 3 dimensions? Is the same result true for solutions of the wave equation? 2. Relevant equations 3. The attempt at a solution Honestly, I have no idea what I am doing. This is all very interesting and it SEEMS like it should be answered by a "oh, yes, that's obvious just do this" quick few lines. But I'm so foreign with my PDE course that this is causing great stress. I need a start, if you can tell me what I should look at, or where I should start, please do so. I will attack it then.