Homework 12 collaboration area
I am not sure how to start on problem number 10 on page 567. Any hint? Thanks!
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
For number 11, page 566 (12.5, 12.6) There is a note in the that says "An is given by (2) in section 11.3" When I go to section 11.3 on page 492, I see (2) and it says y"+0.05y'+25y=r(t)
I am not sure how this applies to the problem. Maybe the reference is incorrect. Can anyone help on this one?
Al
From Eun Young:
I think it's a typo. See (5*) and (6*) in section 11.2 instead of (2) in section 11.3.
Thanks Eun,
Can you please give me a hint on how to apply this to the problem? I was thinking (5*) and (6*) would be A sub n (An) = something, so we could use "An" in the problem.
Al
In regard to problem #4 on page 574 (12.7). How can we integrate (e^-v) Cos (pv)dv? I first looked to see if the functions were even or odd but e^-v is neither so no simplification there. Integration by parts yields another integral that needs integration by parts and it looks never ending. So I am thinking there must be an identity or another method to do this. Any ideas?
Al
