Interim

Always getting crazy busy. Yet another week of hell almost over... only one tough midterm to go. I just spent an hour or so studying for it. I actually get every step to solve eigenfunction expansion problems of seperable PDEs. I guess you touch it a bit in a 2/3rd year PDE course but we're really going into more depth on generalized methods... kinda. Still primarily exponentials, powers and trig functions combined with Bessel functions. Anyway, if you're ever having problems follow these steps:

1) Get homogeneous B.C.s. Do this by finding the 'steady-state' solution where u_t = 0. Solve the PDE/ODE by normal methods for the spatial variables. Let your function u = v - u_ss. This gives you homogeneous BCs for v.

2) Solve the homogeneous PDE, v, for spatial eigenfunctions. Then, let v be the infinite sum of the product of undetermined coefficients in time and the spatial eigenfunctions. Plug this back into the orignal PDE, v. Expand the inhomogeneous part in terms of unknown coefficients in time and the spatial eigenfunctions. Use orthagonality to find an expression for the coefficients. Then, solve the ODE that results from the coeffecients.

I guess I could break 2 down into more substeps but whatever.

What else is new...

Supermileage makes Time magazine's top 50 inventions. I don't know why... but pretty cool.

My work is going well - slow progress but steady progress. The photonic crystals I've made look really nice and uniform. Maybe I'll post a pic sometime.

As a last comment for now, it's good to be free. Next post likely will be after exams O.o

Oh, and if you want some heavy commentary on society, check out my anonymous friend's blog:
http://desolationrow.wordpress.com/