Hi, I've been studying topology over the last semester and one thing that I was wondering about is why exactly is topology defined the way it is?
For a refresher:
given a set X we define a topology, T, to be a collection of subsets of X with the following 3 properties:
1) the null set and X...
yeah that certainly would be a nice result if that were the answer to the problem but theree is a u out front and so a jacobian of 1 will not get the right results, but thanks anyway.
let f be continuous on [0,1] and R be a triangular region with vertices (0,0), (1,0) and (0,1). Show:
the double integral over the region R of f(x+y)dxdy = the integral from 0 to 1 over u f(u)du
I recognize it is a change of variables problem but I'll be damned if I can create a set of...
In my BC calc class, we just finished working through most of series and sequences, and as we were reviewing years past free response questions on the topic, and in 2004, they dropped a lagrange error analysis. I've been looking at different explanations, but I'm not getting the concept. It...
well I1 = I2 +I3 is in the bag. So I guess I'll follow each individual loop to generate the two other equations. And scuttling along with the resistance length and two battery idea, seeing as it will all come out in the kirchoff loop rule wash anyway... I run into some trouble because I don't...
damn, I was almost positive it was going to be two batteries, one for each corresponding loop. As for the currents, would it be I1 traces out the bigger rectangle and splits off into I2 and I3. I2 running up the section we are looking for, and I3 running around the smaller rectangle
I'm thinking three, since it splits at some point. And I meant to make the second Emf negative as well. Now this definitely seems like a kirchoff set up, except that I'm not exactly sure how to play the resistance.
Im thinking if we treat each section like loops, then the current is going...
This one is really getting to me.
Find the current through section PQ (the middle column of the circuit) of length a, a =.65 m. The circuit is located in a magnetic field whose magnitude varies with time according to the expression B(t) = .001t. Assume the resistance per length of wire is...
Two parallel plates having charges of equal magnitude but opposite sign are separated by .12 m. Each plate has a surface charge density of 36 nC/m^2. Determine the potential difference between the plates.
I have to admit I am at a bit of a loss on how to answer this
(lettings S...
I've been working on this problem for awhile but I just can't seem to hack it. (This is problem 76 from Serway 3rd for the first electricity chapter if you happen to have that book and want a visualization)
Given: an electron with charge, -e, and mass, m, is projected with speed v, at a right...
I need to derive the moment of inertia for a solid sphere, but I'm having some trouble.
I did the following.
I=?r^2dm
given density, p= m/V
pV=m
so pdV=dm
and differentiating V wrt r, d(4/3?r^3)dr = 4?r^2
so p4?r^2dr=dm and plugging that in I get
I=?r^2(p4?r^2)dr
I pull the p4...