- #1
AStaunton
- 105
- 1
have been solving PDEs by sep of variables, and the solution that comes out is generally a summation the general look of it is something like:
U=SIGMA(n=1 to infinity)E_n(sin(n(pi)x/L)(cos(n)(pi)x/L)t
The above may not be exactly right, I was thinking along the lines of heat equation where U=temperature x=position and t=time..in most of the basic probs I am doing, a boundary condition is given something like U=f(t) at x=0 or something like that...and this BC is used to solve for E_n...
My question is why when we solve for what the E_n's are do we then use dummy variables to express it...in this case the dummy variable would by t^bar...
The details of what I've written above aren't correct I know, but I hope that that doesn't matter in terms of the question I am asking..
U=SIGMA(n=1 to infinity)E_n(sin(n(pi)x/L)(cos(n)(pi)x/L)t
The above may not be exactly right, I was thinking along the lines of heat equation where U=temperature x=position and t=time..in most of the basic probs I am doing, a boundary condition is given something like U=f(t) at x=0 or something like that...and this BC is used to solve for E_n...
My question is why when we solve for what the E_n's are do we then use dummy variables to express it...in this case the dummy variable would by t^bar...
The details of what I've written above aren't correct I know, but I hope that that doesn't matter in terms of the question I am asking..