Homework 12 collaboration area
From Farhan: This might be a silly question: In the last step of finding a solution to a wave or heat equation, why do we take a SERIES of the eigen functions, and then incorporate the initial condition to get the solution of the entire problem. I know that, sum of the solutions (eigen functions) is also a solution to the PDE, but in the last step, what if we work with ONLY ONE eigen function and impose the initial condition? Will that be wrong?
Farhan, I think the series of the eigenfunctions is needed to satisfy both the boundary conditions and the initial conditions (as stated on p 548, a single solution will generally not satisfy the initial conditions). I think it would be hard to come up with a single function that satisfied both (other than the zero function). Please correct me if my thinking is wrong here! -Mjustiso
