Recent content by Physics-Pure

Would you mind showing the work required for (1)? Using the ratio test

"phi and conjuagte phi are the roots of 1-z+z^2 It works out the same in the end." Why does it work out the same in the end?

Why is it even relevant to the question at hand?

Alright. Can you also tell me why it's even useful to show that it has a positive radius of convergence? And how to do so?

Why would dividing by z^(n+1) extract the a_nth term?

Ahh, I understand. Now why did you put -phi and 1-phi instead of phi and conjuagte phi?

First off, where does the z^n+1 come from? But I believe I understand the rest now.

If you would like to see my work thus far on this problem set look here: http://math.stackexchange.com/q/282436/58540

If anyone knows where to find the solution set, that would also be appreciated. It isn't homework related, simply for fun.

Hey guys~ I was looking for a way to derive a formula for fn (the nth term in the fibonacci sequence). While looking for this, I came across a potential solution using the residue theorem. Using the generating function Ʃk≥0 fnzn, find the identity for fn. The problem looks like the right...

Hi Guys~ I was wondering if anyone had any suggestions for applications of the Kelvin-Stokes Theorem. Recall that the Kelvin-Stokes Theorem states: http://upload.wikimedia.org/math/0/4/4/04402b2d910114267bffa0e030445af6.png (Check Wikipedia for further explanation) Obviously one could...

Where did that y(x) come from? And are you saying that we let y = y(x)dy/dx)dx? P.S. I was simply following the "Introduction to differential equations" video, under calculus. Found here: http://www.hippocampus.org/Calculus%20%26%20Advanced%20Math;jsessionid=BAEE0BB1E88F4A594768EEBE4D8FC1EA

Hello all~ Given the equation: dy/dx = (x/y) I know we would initially go to: ∫dy =∫ (x/y) dx then too: ∫(y)(dy) = ∫x dx Until arriving at: (y2/2) + C1 = (x2/2) + C2 (y2) - (x2) = C My question is: Where does the dy disappear to in step 4? Where the anti-derivative is taken...

Why does the anti-derivative take the form (integral symbol) f'(x) dx?

When is dy/dx allowed to be treated as a fraction apposed to an operator? What properties of the integral symbol allows a function (y prime) to be transformed back to f(x)?