domains Definition and 114 Threads

Homework Statement f(x,y) = 1/(x^2 + y^2 -1) 1. For what domains is f continuous? 2. For what domains is f a C^1 function? (Here C^1 means that the first derivatives of f are all continuous) Homework Equations The Attempt at a Solution I would be very grateful for the help...

So here are some functions of the following types... f: R -> R^2 (curves in the plane) f: R -> R^3 (curves in space) f: R^2 -> R (functions f(x,y) of 2 vars) f: R^3 -> R: (functions f(x,y,z) of 3 vars) f: R^2 -> R^2 (vector fields v(x,y) in the plane) The question is - why are curves...

We are asked to find a branch where the multi-valued function is analytic in the given domain. The function: (4+z^2)^{1/2} in the complex plane slit along the imaginary axis from -2i to 2i. The principal branch is \exp(\frac{1}{2} Log(4+z^2)) and so we want analyticity from -2i to 2i. It seems...

I have a problem solving this equation for x - finding the maximum domains. 3(2^(2x+1)+5(2^(-x) )= 31 What I did first was to take the logarithim on both sides of the equation... to solve for x. But that apparently isn't a "logical" way to proceed. Any advice?

What are magnetic domains made of? How small are they compared to an atom?

Just need a quick clarifier. If I purchase a domain name, and I have any ISP that gives me an email address, is that all I need to be able to establish an email address (by aliasing I presume) with my new domain ? Example: 1] I'm paying $9.95 for dial-up service on cheapoISP.com, so my...

Hi, Could someone please help me out here? state the implied domain and range of B) tan (2arccos(x)) ok, the domain of tan for which arctan exists (conventionally) is (-pi/2 , pi/2) -- really the domain of tan is R, but we're using the restricted one. therefore, we know that the...

If S is a domain that is simply connected for S not equal to complex plane and z is in D. Assume g maps D into itself and f(z)=z. prove |f'(z)|<=1 how should I do this? nowhere near the desired result.. help!

In ferromanetic materials like steel , molecules adjacent to each other will align themselves and "pull " in the same direction.When enough domains have their North poles facing in the same direction they collectively produce a magnetic field. So how does that actually happen ? Does it have...

I'm suppose to find an integral domain where NOT every element (not a unit) is expressible as a finite product of irreducibles. I'm not sure where to begin, actually. So perhaps someone can give me a tip, and we can start working our way through this. Thanks..

this seems to be a very fundamental problem...but i need help... prove or disprove : let D be a euclidean domain with size function d, then for a,b in D, b != 0, there exist unique q,r in D such that a= qb+r where r=0 or d(r) < d(b). first of all, what is size function? next...do we only...

I'm working on solving coupled PDEs (mass diffusion - heat transfer - continuum mechanics) in problems where the solution domain changes depending on the solution (call it an intrinsic coupling if you will). This happens either due to addition of material to the domain or damage of the domain...

How can companies sell domains names, i mean how do they own it-- is there a way to get them for free. How come we have to pay for them by the year.

I'm lost! My book of topology says that its possible to construct a (continuous!) function f:[0,1] -> R^n such that the image is a ball {x: |x|<=1} I can't imagine how is it any possible to do such things. The book doesn't give any example or prove of it. It's just a comment. Any ideas? I...