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Today I learned something of Calculus
Since the slope of a line is determined by (Change in Y)/(Change in X), it would seemingly be impossible to determine the slope of a curve at a single individual point. Using a concept introduced in Calculus, however, called a Limit, one can find trends in the Value of f(x) as X approaches a given number to kind of simulate what X would be if it could exit, such as in instances where a denominator of 0 makes f(x) impossible to actually determine. Using this concept, Derivatives are created. Using a formula derived from the slope formula, one finds what the slope of X moves towards as the Change in X gets smaller and smaller until it finally reaches 0, giving the hypothetical slope at a single point.
OR, IN ENGLISH Since it is literally impossible to find what the slope of the tangent of X is at a single point, since you can't divide by zero, you use some DERIVATIVES and some LIMITS to find what the slope WOULD BE EQUAL TO if it WERE possible to find it; Thus accurately stating the value of the slope at X. What the fuck Calculus. What the fuck. EDIT: OH YE GODS MY BRAINS HOW DO YOU FIND THE AREA OF INFINITY RECTANGLES EACH WITH A WIDTH OF ZERO!? EDIT AGAIN: I was about to Seil Tag this thread, but I think an SMB tag would be much more appropriate. |
Professor Calculus is in someways a metaphor for the contract of literature,the lie of literature- he inverts the literal conventions that his fictitious companions take as pat and ths opens up new spaces of the textwhile also shutting them down- questioning and yet maintaining the core secret. His rather trivial little pendulum takes him directly here, directing him on circular paths that would otherwise be straight, enabling a greater variety of experiences to be drawn while also asking questions of the straight path. Castiafore sings a song but Calculus plays along.
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Or yeah, integrals. Math is easier when you stop wondering why and just accept that it works. Makes Legendre polynomials a hell of a lot easier on the brain. And fuck Bessel functions. |
I sit in the back of the class and watch their dreams shatter on the chalkboard.
They're so cute before they start messing with real calculus and not this sissy two dimensional junk.
Their eyes are so full of hope, all a-twinkle with knowledge and optimism. And then they're asked to integrate in three dimensions using spherical coordinates or some other silly process and you can just...see them break. It's my own personal meth. |
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Dude spherical coordinates ain't that bad, neglecting the harmonics. It's the cylindrical coordinates. Those are terrible. As I said before, fuck Bessel functions.
Also, axial symmetry is <3. r^2 sin theta dr dtheta dphi becomes 2 pi r^2 sin theta dr dtheta so easily :D |
Oh yeah, I personally don't have a problem with them. I actually prefer them for a lot of applications over rectangular coordinates. They can make things plenty easier depending on what you're doing. Seconding the mad diss on cylindrical though.
It just all them other folks seem to think that other coordinate systems are their bane and to be avoided at all costs. |
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That always confused me. I mean, if the situation supports noncartesian coordinates, they may well be worth a shot. I'd hate to imagine determining the potential of a spherical charge distribution through rectangular, especially if it lacked axial symmetry.
I mean, hey, a lot of math makes a hell of a lot more sense in the respective coordinate system, just like some unit conventions make other things easier (I hate cgs, but damn do magnetic moments just pop out of it). Also, to the above: chain rule is <3 |
I find it hilarious that before they had scientific calculators they had to rely entirely on memorizing those giant formulas you see in movies with scientists doing sciency-stuff.
As you well may know (which is to say you would not, since I probably haven't mentioned it, or if I did no one cared), I stopped at Trig because Calculus made my brain hurt for the year of high school I took it. |
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Okay, what you just described? Is nothing. I spent today putting data into a 3x3x3 matrix because the data collector didn't think to hold anything constant when he got the data. I then had to take this three dimensional matrix, derive it, graph it and see if it fit inside of the expected outcome to a reasonable degree.
Just let it keep going, the stuff you will do with calculus is going to be the more important stuff you will ever do because you don't always work with statics. Here's a fun question for the original poster too, at least an arithmetic question that somehow no one gets told: Why does x^0 equal 1? |
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X^2 equals X*X*1 X^1 equals X*1 X^0 equals 1 I mean, sure, by definition of a square or power, there isn't really a 1 there, but I was always taught that everything could always just be implied to be multiplied by 1 as many times as it takes to make simplifying easier. I guess in more mathematical terms, the way you subtract a power from an exponent is dividing by an exponent of the same variable. Meaning that the way X^2 becomes X^0 is by dividing X^2 by X^2 producing X^0, which equals 1. |
And yet I majored in and study a science.
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I miss my innocence.
I remember back in the good old days when the most complicated thing I had to do involve functions, or vectors, or trigonometry.
Sines were sines, cosines were cosines and I didn't have the slightest clue what a limit was beyond FFVII. Then I learnt calculus. And I've never had a peaceful night's sleep since. Not even the hard stuff that Tahr was talking about, either. |
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The point is that I am the grammariest.
ha ha
That actually sounds better than what I has assumed at first -- that you had meant, "know", which just made that sentence a little weirder-flowing on top of that. ALSO. I still have calculus books from courses despite not being a mathematics major. That shit was fun even if I couldn't solve it all anymore. e: Retarded to study for, kind of like being forced to know NP-Complete proofs, but yeah... |
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x^1 times x^-1 is x^0. But (x^1)(x^-1) is the exact same as writing (x^1)/(x^1) and like you said before that equals 1. |
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