Thread: I like calculus

Originally Posted by DavidP

I like Calculus but I hate my Calculus teacher with a passion. If you ever go to BYU, take Calculus from any other teacher than Dr. Skarda. Just a tip for anyone who ends up going there.

Thanks for the tip :P

I'm only in Algebra II, but, I've got three more years in high school...

How many calculus courses are there? I know our high school offers AP Calc I and II, both of which I'll be taking, but how many more are there?

Holden, use integration by parts. Let u = x, and dv = e^(2x)*dx

Originally Posted by holden

Calc is awesome, I just took the calculus AB AP test, and I'm pretty sure I got a 4 or a 5...oh wait I'm not supposed to talk about that lol

Next semester for my senior high year, I get to take Calc II!!!! YEEEAHHHH!!!!

Oh and btw, I keep getting the wrong answer for the integral of (x)(e^2x)

Can anyone show me how to do that one?

Here's what I did...

u = e^2x
du = 2e^2x dx
x = 1/2 * ln|u|

so... (S is the integral symbol)

S (x * e^2x) dx

1/2 S (2x * e^2x) dx

1/2 S (1/2 * ln|u|) du

1/4 S (ln|u|) du

1/4 (u * ln|u| - u + C)

1/4 (e^2x * ln|e^2x| - e^2x + C)

1/4 (e^2x * 2x - e^2x + C)

x/2 * e^2x - e^2x + C

Hmm.. I think I did that right :/

ah yes, im so stupid sometimes....

i was doing u=e^2x...

actually, heres the answer (and its correct)

S x * e^2x

u = x

du = 1 dx

du = dx (this is where the x goes out w00t)

dv = e^2x

v = e^2x / 2

vu - S v du , so:

(x * e^2x) / 2 - S e^2x / 2

((x * e^2x) / 2) - (e^2x / 4)

and finally:

(2x * e^2x - e^2x) / 4

And I checked it on my buddy (TI-83 Plus)

Oh and another question...integration by parts works fine, but is it possible to solve with straight up u substitution?

I couldn't get an x to cancel out with just a u substitution (which is all we learned, I learned integration by parts with this book my calc teacher lent me)

I hate to say it but my high school calculus class hasn't even covered substitution by parts. I've read ahead and can do it myself, but my class is just retarded. I should've taken AP calc, I would've done well, but oh well.

I have an incredibly easy time knowing the "right stuff to do" in order to get really really freaking high grades in calculus, but, like, I want to understand things at a really fundamental level. I always want to read *every* proof and memorize it and understand why it works and know how to derive it in my sleep. I've even got sick of not knowing how sqrt, sine and cosine works on my ti83 so I read how to do it and programmed my own sqrt sine and cosine functions! I admit however that for things like product rule and quotient rule I just memorized, but that's obsolete now that we're doing ln differentiation. I am a pain in the ass to teach, because every 30 seconds while my teacher is talking I'm like "explain that again" .

so, like, I think I read somewhere that zach is going to mit. is that true? If so, that's really freaking awesome. What kind of stuff are you guys doing? I want to be in really really really hard classes next year and if I'm not I'm going to drop out or kill everyone.

EDIT: when I said 'what stuff are you guys doing' I was kind of asking everybody that thinks they are in a fairly high level math course.

Here's a program I wrote earlier in the year for one of our portfolios. What it does is you enter a script file defining a polynomial equation (doesn't work transcendental equations), enter the limits of integration, then enter the number of subdivisions, and estimates the value of the interal and the length of the curve numerically and it draws the function.

You have to adjust the camera position using the arrow keys to move around and the + and - to move in and out.

You must hit 'A' to tell the program what script file to open. I included a few to show how the syntax works. It's not overly useful because it's so easy to find the value of integrals with polynomials but oh well, this was more than expected for a high school class.

Multivariable integral or diferential calculus are nice, i like them, maths are my big passion (after my girl).
I wish i could have more maths courses... unfortunatly i complete all of them two years ago
let me just try that primitive...looks like a two-part primitive...

http://www.calc101.com/


This site helps me out so much with derivatives. It does integrals, too.

Silvercord, you heard correctly. It really is gonna be awesome.

I've always thought that the abstract algebra is quite fun. Granted, it doesn't have too many direct practical applications, but the idea of abstracting classes of numbers into various sets (of anything) and operations upon sets is quite fascinating. The neatest proof that I have seen in algebra (and the reason the theory was developed anyways) is the proof that not all roots of polynomials of degree five or more can be expressed in terms of radicals.

Zach have you dealt with Inertia tensors a lot? I need help. I'm working on implementing torque for a 3D engine, such that when objects touch linear and angular impulses are generated (I've got linear impulses, that was fairly easy, and it takes into account estimated coefficients of restitution, oh yeah baby!). It's easy when doing torque in 2D because the inertia tensor reduces to a scalar, but, in 3D it is a freaking 3x3 matrix or a quaternion, and like, I don't get it, lol.

EDIT:
Im silvercord