Engineering and Applied Sciences Applied Physics 216 Lecture 7: Lecture 7
21 Feb 2017
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Document Summary
Ap 216 lecture 7 series solutions for potential functions, orthogonal functions and. What we have to say started with fourier"s studies of the heat equation . It follows from the conservations law for heat (when no work steals it) which is f is the heat density and j obeys fick"s law (except at very low temperatures) which embodies the notion of randomness and diffusion. So in one dimension which under steady state conditions looks a good deal like the le steady state conditions. Fourier observed that linear equations like the above together with their boundary conditions could be solved with the help of infinite sets of functions that were orthonormal and complete like sines and cosines. Assume that x f x a u n n n. U x u x x x n n n n. When this is true the an"s are obtained from orthonormality by multiplying by un" and integrating to give a n n.
