Recent content by podboy6

Wouldn't a sphere with one disk removed look like a disk? (For instance, chopping off the lower hemisphere or at least cutting a hole and stretching it out to a disk?

Homework Statement What is the fundamental group of A where A is the 2-sphere with two disjoint disks removed. It has the same homotopy type as a familiar space.Homework Equations The Attempt at a Solution When I first looked at this problem, and saw how it was drawn out (in Munkres book,) it...

Well, for the first part, given that |p(z)| \leq|M| for |z|=1, and with: p(0)=a_0 p'(0)=a_1 p''(0)=2a_2, then in general, |p^k (0)| \geq \frac{k!}{2\pi i} \int_{|z|=1} \frac{f(z)}{z^(k+1)} dz \Rightarrow \frac{k!}{2\pi i} \int_{0}^{2\pi} f( e^(it) ) dt \leq k!M. thats about as far...

okay, it should be |a_i| is less than or equal to M for i=0,1,2.

So my professor threw in what he called an extra 'hard' question for a practice test. So naturally I have a question about it. It relates to the Maximum Modulus Principle: a) Let p(z) = a_0 + a_1 z + a_2 z^2 + ... and let M = max |p(z)| on |z|=1. Show that |a_i|< M for i = 0,1,2. b)...

Okay, so I have a homework problem I'm a little confused about, The textbook is pretty useless and we didn't go into types of orders very much in class. So, am I to show that the dictionary order is reflexive, antisymmetric, and transitive on XxX, since XxX is already linearly ordered? I...

My proofs professor gave us this problem as a challenge, but I'm stuck, which is why I'm here: Let A,B sets Define set A to be (0,1) Define set B to be P(N), where N is the set of natural numbers, and P(N) is its power set. Question: Construct a bijection between (0,1) and P(N) or a...

Worst math joke ever: "Okay, when you rotate a conic section, you slap on -iod to the end of its name, i.e, paraboloid, hyperboloid, ellipsiod, ect... Okay, what do you get when you rotate a human? A humaniod."

ok, so then: \Sigma\overrightarrow{F_3} = \overrightarrow{F_{13}} + \overrightarrow{F_{23}} = 0 \frac{1}{4 \pi \epsilon_{0}} \Large [ \normal \frac{|q_1||q_2|}{(2L)^2} + \frac{|q_1||q_2|}{L^2} \Large ]\normal = 0 is this sort of on the right track? I wound up getting q_2 =...

For the electrostatic force to be zero from particles 1 and 2, then shouldn't,#1 both 1 and 2 are electrically neutral and particle 3 is charged, #2 particles 1 and 2 are charged and particle 3 is neutral, or #3 all particles are neutral? If #1 or #2 are the case, then as particle 3 moves...

Just got out of my E&M class lecture about Coulombs Law, I'm having trouble getting off of the ground with an electrostatics question: Question: Three charged particles lie on the x-axis (fig. 1). Particles 1 and 2 are fixed. Particle 3 is free to move, but the electrostatic force on it...

Hello everyone, I was wondering if someone could take a look at two equations to see if I am solving them properly. I'm currently in Calculus II, but is been a year since I took Calculus I (budget cuts canceled the Calc II class last spring,) so I want to make sure I still haven't forgotten...