Why Use Orthogonality Properties in Special PDE Problems?

[jgthb]

Hello

I have been wondering for some time about, why I have to use orthogonality properties in a special kind of PDE problem I have encountered a few times now.

As an example see exercise 13-3 in this file:
http://www.student.dtu.dk/~s072258/01246-2009-week13.pdf"

I have described my thoughts on this in this file:
http://www.student.dtu.dk/~s072258/ortho_comments.pdf"

And I have solved the problem in this file (the right way by use of orthogonality properties):
http://www.student.dtu.dk/~s072258/orthogonality_solution.pdf"

The last file is in danish, but part b) (which I comment on in the second file) almost only consist of calculations, so it shouldn't be a problem.


Some insight would be much appreciated :)
Jonathan

 

[jgthb]

okay, think I found out why it doesn't work.

The derivative of a function is not equal to the derivative of the function's Fourier Series in general. So obviously my method won't work.

example:
http://www.advancedphysics.org/forum/showthread.php?t=7278"