Recent content by notmuch

tjackson3, is x a real variable?

Euler's Formula I did not attempt this, but have you tried using Euler's formula to help simplify before plugging in the series?

A re-statement of the problem and my work (so it's easier to read): Let \gamma(t) = re^{it} for t \in [0, \pi]. Evaluate: \lim_{r \to \infty}\int_{\gamma}{\frac{e^{iz}}{z}} So far I have: \int_{\gamma}{\frac{e^{iz}}{z}} = \int_{0}^{\pi}{e^{-r \sin t}(\cos(r\cos t) + i\sin(r\cos t)}dt So...

Complex Analysis--Path Integral Homework Statement Let I(r) = Int(e^(iz)/z) over the "top half" of the circle of radius r, centered at the origin. Show that lim {r -> infty} I(r) = 0. Homework Equations All given. The Attempt at a Solution I was thinking of using the inequality...

elle, What conditions do you need on a, b, and c in order to make the identity? Are they within the constraints of this set? I think so. Just choose those values of a,b,c. In order to show inverses exist for every element of the set, you know something regarding determinants that guarantees...

Matt, Sorry for the confusion. I was a little confused by your response so I didn't reply, I was trying to see if I was understanding you correctly. AKG expressed what I meant to say. You're right about the Hausdorff/compactness conditions... we are stuck with finding both X and Y being...

Matt, I understand that. I was not refuting the fact that those two topoligies are not homeomorphic. Finding such examples of non-homeomorphic spaces is easy, but finding the functions satisfying the conditions is the hard part.

HallsofIvy, Thanks for the reply, but that won't work with this definition of continuity: f:A->B is continuous if f^(-1)(U) is open in A for every open set U of B.

Hello, Here's a problem that I'm having trouble with: Give an example of metric spaces X and Y and continuous maps f: X->Y and g: Y->X such that f and g are both bijective but X and Y are not homeomorphic. I can find plenty of examples where I can find one such function, but finding...

Unit_circle, At my previous University, there was a McNair Scholars program. I did research and attended undergraduate research conferences, and many of the McNair Scholars were there as a group. At that university, the program focused quite a bit on research and giving undergraduates...

Calculus is a very good self-study topic to learn for a high schooler. If you are able, then do it. Because of some schedule problems, I could only take up to pre-calculus in high school. I talked to the AP calculus teacher, said that I would want to study for the test and take it... he...

Got it. Thanks a lot!

Hello. I am given the following: T([1,2,-3]) = [1,0,4,2] T([3,5,2]) = [-8,3,0,1] T([-2,-3,-4]) = [0,2,-1,0] And of course I know that: T(x) = Ax and I want to find the matrix A. So, from the individual equations, I construct: A[1, 2, -3] = [1, 0, 4, 2] (please forgive, these...

Wow! This forum truly makes me feel at home. This is my 3rd semester at the University. I had originally planned to concentrate on Chemistry, but I've been considering more and more dual majoring in Math. Plus, since I am pretty far ahead in my Chemistry requirements, my school has a dual BS/MS...

Hi. I am wondering if there is a program that can do a few things: 1. Plot data points 2. Graph functions 3. Show math symbols (integral, etc) with correct placement of characters I am attempting to do these things in a lab writeup, so if separate programs are needed I would need to...