Friday, November 16, 2007

Don't try this at home folks.

That is waking up at 2:30 and then dropping dead until 3am, and then finally crawling out of bed after muttering a few expletives! And boy is it cold at this time.

I haven't started revising stats yet, but will begin at 4am. Just had some weetabix, and then decided to have toast too. Leaving the bread in the toaster I lost all sense of smell, and five minutes later the whole kitchen was smokin'! So toast it is then.

Two tests today have forced me to wake up earlier than usual. Don't worry I am "experienced" at this and have been doing this for many many years. (Year 8 is how far back I remember doing this). Therefore, as I said above, do not do this unless under supervision.

What will become of me today, I don't know. Will I manage to stay awake in the test, or will I starting walking in the clouds? I think I will manage, but one test is just before Algebra and the other an hour after! Why must these things happen? We will be starting rings today as well.

I hate stats and PDEs: it's officially official now! Now for a want of disliking things, but because I am very 'perverse' and hate having only an artificial understanding. I started liking mechanics more because my lecturer brilliantly enhanced our understanding of things. Fizz and myself were commenting on how cool some lectures had been. And then you have PDEs. I can't believe I am saying this, but at the moment stats is the lesser of the two evils.

Hopefully it won't remain like that forever! I think I have finally understood "separation of variables" and eigenfunctions.

When we solve for eg. functions of the form u(x,t), then most of the times their solutions are of the form u(x,t) = X(x) T(t). That is, u(x,t) is a product of a function of x and t. For the separation of variables thing, we suppose that the solution IS of that form and then do our business depending on the PDE.

Once the substitution into the PDE etc is over, we might have something like X''T = T''X, i.e. X''/X= T''/T; one side with t's and the other with x's. (I have dropped the T(t) notation and just wrote T).

The bit I wasn't getting: whatever value t is inserted into the right hand side does not have anything to do with the left side. The left side remains constant, so we might as well just write the right hand side as T T'' = mu (1). Similarly the same applies to the values of x into the left hand side, so again we get X''/X = mu (2). We now have two ODEs, instead of a horrible looking, ugly (etc) PDE. ODEs are 'relatively simpler' but somehow because of the darn PDEs flying about I don't feel that way. (This all sounds dodgy so don't take my word for it). If we rearrange (2) to give X''= Xmu, then mu is the eigenvalue and X is the eigenfunction!

Imagine having an "aha" moment after reading the above, and then imagine seeing Fourier series pop their ugly head around the door. That is enough to shatter anyones confidence.

I am really having bad vibes about these two exams, namely due to my artificial understanding of the subject. In the other four tests I had an idea, a picture, of what was happening. In these two modules I am having a stinker of a time. Tomorrow is officially going to be my worst day. Damn me - I mean today!!

OK, that is enough from me. Back to the stats and tea it is.

PS: The irony. (link of "sleep deprivation", not that I have had the chance to properly see it).

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