More integrals, quizzes, plus a meme
Apr. 25th, 2003 06:21 pmAd Mundo Exteriore,
Follow-up report on the math problem of the Lord Kelvin quote. After solving the silly thing, I realized that indeed it should be obvious to anyone who has taken first-year calculus or statistics that the integral from 0 to infinity of e^-u² with respect to u is equal to the square root of π divided by 2. Why? Because that function is a variation on the Boltzmann distribution, yes, my friends, the famous standard bell curve. Sheesh. Also, it turned out to be a really simple problem. After applying change of variables and squeezing theorems, it practically fell in my lap.
Sometimes I think I'm getting the hang of this course. Then I'm asked to show that the tangent vector to a point on a three-dimensional surface is orthogonal to the outward normal vector at that point, and I realize that I don't and I never will. ::sighs:: (I mean, you would think that it's in the definition of tangency, right? But no, apparently it needs to be proven! Proving the obvious is always ten times as difficult as proving the obscure. Let that be the moral of the day.)
It took me four hours to do the last four problems. That's an hour per problem, isn't it? D'you know what's especially infuriating? Calculating a horribly complex surface integral with long strings of cosines and sines in the Jacobian determinants and then having it all reduce to 0. I suffered for one hour in order to calculate zero. Argh! ::very disgruntled::
You wouldn't think it would be so complex, but there is no nice and easy way to parametrize a sphere. The long strings of cosines and sines, as painful as they are, are much easier to differentiate and integrate than the square root of r² – x². Oh well.
Courtesy of
tryogeru

You come from Dark Water. You are solitary and find peace in yourself, or maybe you're
turmoiled but pull off peace.
Where Did Your Soul Originate?
brought to you by Quizilla
Not only is this quiz stupid, it has a hundred grammar mistakes and has bad diction. But the picture looks pretty, which is somewhat mollifying.
Oh, and I picked up this meme from
durberville, who wrote something nice about me and put me in a good mood. So I feel I should pass it on, somehow. ^_^
To friends, thank you...
aetherangelette, for being my evil older brother and my main source of illegal anime ^_~ (though she never uses her LJ)
bottledgray, for being my evil older sister and co-conspirator in our many plots and schemes to change the world (doesn't use her LJ either, unfortunately)
crazed_tenshi, for keeping me on her friends list even though I've been delinquent in giving feedback (will do better in the future!)
durberville, for being one of the best writers I know and for not giving up on Liebestraum and Bean Sidhe ^_^ (sorry to hear that you'll be gone, but I hope you'll be back soon, with even more writing to share!)
fyredancer, for writing the first 1x2 fic I've ever read and for prolific LJ entries that amuse me on Friday afternoons
kaydeefalls, for being the master of irony, for never failing to make me laugh, and of course, for being a good friend
keelywolfe, for writing Harry/Ron and for her rants on bad grammar and fanfiction cliché
lazulisong, for making me look for DN Angel and KKJ manga
ldmoonflower, for the subway cars of insanity, for the HPTF conspiracy, and for being willing to listen to my self-pity
lianara, for liking Ender's Game and anime and for joining the Society ^_~
lush_rimbaud, for being one of my best friends and for always being ready to discuss the three essentials: books, art and her latest crush (just kidding about that last one)
pornkings, for being such a brilliant writer and for posting LJ entries that make me think
trivetmonger, for being the composer of many classic songs and jokes that shall never be forgotten in the annals of the Hallway
tryogeru, for always keeping in touch, for being my other main source of anime, for agreeing to keep me company at prom, and for introducing me to Hikaru no Go (for which I will forever be grateful ^_^)
Well...look at that. I have more friends than I thought. That is strangely comforting, considering my usual state of being a self-imposed hermit.
Will be gone 'til Tuesday, due to a scheduled visit to Cambridge, Massachusetts. May there be many LJ entries and an extra Hikaru no Go episode released on TW before I return.
...Tari
Follow-up report on the math problem of the Lord Kelvin quote. After solving the silly thing, I realized that indeed it should be obvious to anyone who has taken first-year calculus or statistics that the integral from 0 to infinity of e^-u² with respect to u is equal to the square root of π divided by 2. Why? Because that function is a variation on the Boltzmann distribution, yes, my friends, the famous standard bell curve. Sheesh. Also, it turned out to be a really simple problem. After applying change of variables and squeezing theorems, it practically fell in my lap.
Sometimes I think I'm getting the hang of this course. Then I'm asked to show that the tangent vector to a point on a three-dimensional surface is orthogonal to the outward normal vector at that point, and I realize that I don't and I never will. ::sighs:: (I mean, you would think that it's in the definition of tangency, right? But no, apparently it needs to be proven! Proving the obvious is always ten times as difficult as proving the obscure. Let that be the moral of the day.)
It took me four hours to do the last four problems. That's an hour per problem, isn't it? D'you know what's especially infuriating? Calculating a horribly complex surface integral with long strings of cosines and sines in the Jacobian determinants and then having it all reduce to 0. I suffered for one hour in order to calculate zero. Argh! ::very disgruntled::
You wouldn't think it would be so complex, but there is no nice and easy way to parametrize a sphere. The long strings of cosines and sines, as painful as they are, are much easier to differentiate and integrate than the square root of r² – x². Oh well.
Courtesy of

You come from Dark Water. You are solitary and find peace in yourself, or maybe you're
turmoiled but pull off peace.
Where Did Your Soul Originate?
brought to you by Quizilla
Not only is this quiz stupid, it has a hundred grammar mistakes and has bad diction. But the picture looks pretty, which is somewhat mollifying.
Oh, and I picked up this meme from
To friends, thank you...
Well...look at that. I have more friends than I thought. That is strangely comforting, considering my usual state of being a self-imposed hermit.
Will be gone 'til Tuesday, due to a scheduled visit to Cambridge, Massachusetts. May there be many LJ entries and an extra Hikaru no Go episode released on TW before I return.
...Tari
(no subject)
Date: 2003-05-03 12:53 pm (UTC)::mutters:: Evil older brother -.-;;
Re:
Date: 2003-05-04 08:04 am (UTC)Yes, and go check your LJ more often. I talk about you a LOT in here.
...Tari
(no subject)
Date: 2003-05-04 11:24 am (UTC)~_~;;