Instructions...
Download this addon for firefox.
Latex Composer
https://addons.mozilla.org/enUS/firefox/addon/4082/
For the unaware, Latex is a universally used typesetting software for maths documents.
Now look at the very bottom right of your browser.
Should be a small round symbol thing like this > .
Clicking this brings up the compiler.
Now you can enter code that produces math output.
Now posting the code here won't convert it into math output since this site doesn't have Latex installed but...
If you just copy and paste the code here, others can again copy and paste it into the compiler to see your formulas and what not.
So folks... Whats your maths experience? Area of interest etc!
For me,
Dynamical system, methods of integration, asymptotic methods and maths biology are my areas of interest. Just graduated 2 weeks ago. Feels good man... Going for a masters now as well.
\Gamma(z) = \int_0^\infty t^{z1} e^{t}\,dt


07132010, 03:23 PM #1
Math thread! Come in and have some pi...

07132010, 03:28 PM #2

07132010, 03:36 PM #3
Being from UK I'm not quite sure what Calc 1 and 2 are... Perhaps an example of what's in it?
As for maths biology...
It's basically a combination of dynamical systems and differentiation.
I wouldn't have thought you would have covered dynamical systems yet but...
From wiki
The dynamical system concept is a mathematical formalization for any fixed "rule" which describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake.
So basically how stuff changes as parameters change.
Like populations. And you find limiting populations, where any more people/things introduced into the environment will cause them to die out due to resources etc.
Stuff like that!

07132010, 03:41 PM #4

07132010, 07:30 PM #5

07132010, 07:37 PM #6

07132010, 07:44 PM #7

07132010, 07:46 PM #8

07142010, 03:21 PM #9

07142010, 04:00 PM #10
 Join Date: Aug 2009
 Location: United Kingdom (Great Britain)
 Age: 30
 Posts: 1,152
 Rep Power: 798
The fundamental idea of partial derivatives is any function which isn't being partially derived is treated as a constant.
eg, supposed a function such as
f(x) + f(¬x)  (¬x == not x).
the partial derivative treats f(¬x) as a constant, so, the partial derivative of the function becomes
f'(x)
remember the derivative of any constant is 0.
So going back to your question, observe that your function has two parts
15y = f(y)
sqrt(x) = x^1/2 = f(x)
so the partial derivative d/dx of 15y + sqrt(x) = d/dx f(y) + f(x) = f'(x) = 1/2 x ^(1/2)If you do what you've always done, you'll get what you always got

07142010, 04:10 PM #11

07142010, 04:50 PM #12

07142010, 07:28 PM #13
Could someone show me, step by step, taking the partial derivative of the CobbDouglass function? Need to learn it for econ..
Y = AK^a L^1a
a = alpha.
With respect to K, and then respect to L.
I know what the derived functions should look like, but can't figure out the steps. How do you take a partial derivative when there is not an actual number involved, like alpha, above?

07142010, 07:44 PM #14

07142010, 11:04 PM #15
geometric topology is a pretty big field. i'm still 2 years away, so right now i just read a lot of literature (there's no textbooks at this point... just papers) to try and learn the material. focusing primarily on coxeter systems, mostly just because that's what my major advisor is interested in, lol.

07152010, 12:06 PM #16
When differentiating with respect to K here (for example), treat everything else as a constant.
So just remember the rules...
If f(x) = x^k
Then f'(x) = kx^(k1) (see here http://en.wikipedia.org/wiki/Derivat...tary_functions)
In the K case, it would be.
Y = AK^a L^1a
Derivative with respect to K is...
AaK^(a1)L^(1a)
(To view a better version paste the below code into the addon compiler from the first post)
A \alpha K^{\alpha1} L^{1\alpha}

07222010, 06:13 PM #17

07222010, 06:29 PM #18
The farthest I ever got was the 2nd semester of differential equations.
Both I thought were pretty easy compared to the hell that is Calc II.
Calc II largely is dependent on the teacher teaching it. My first time attempting Calc II we had a new teacher to the university from Harvard and he wrote the text book. This guy had crazy ridiculous standards. He didn't even give partial credit on tests. It was either all right or all wrong. I am so glad I dropped that class and made it up over the summer.

07222010, 06:35 PM #19

07222010, 06:39 PM #20

07222010, 07:00 PM #21

07222010, 07:32 PM #22
They won;t cover it... actually I am not even sure they cover it in any undergrad course.
How they work is:
Suppose you want to take the derivative of a function f, call it Df.
Then D is an *operator* that maps a function f to another function Df.
We write this as f > Df, kinda.
If you want to find a 1/2 derivative, then the idea is to find an operator H such that
H^2= H H = D. Then applying H to f to get f > Hf we would say that Hf is the half derivative of f.
actually just wiki it, they have latex and explains it pretty well

07222010, 07:50 PM #23

07222010, 09:21 PM #24

08072010, 08:02 AM #25

08072010, 08:06 AM #26

08072010, 08:48 AM #27

08072010, 11:37 AM #28
Ah cool. How's number theory going? I found it mind boggling but ended up doing pretty well in it. What's in foundations of maths, epsilondelta proofs?
Yeah, but! Read my OP again. It's a add on that lets you preview latex within firefox. Download the add on, type up some math in it, then paste the code for it here. Others can then copy and paste the code into the add on to see your formulas.

08072010, 01:17 PM #29
 Join Date: Sep 2007
 Location: Tallahassee, Florida, United States
 Posts: 25,767
 Rep Power: 25854
foundations of math is essentially learning different techniques of proofs and when to use which ones. number theory was good man finished with an A. was harder for me at the beginning because i have never had a proofbased class before that, but i got it down by the end.
**** Football Crew
TB Lightning

08072010, 02:20 PM #30
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