Domain Definition and 704 Threads

Hello everybody! I am trying to construct the FDFD method for 3D structures. I have already constructed the general formulation and specifically I have set the complete matrix form. Due to the fact that the matrices are too sparse, and my system is out of memory, I am trying to set the problem...

In other words, is the domain of a function by definition non-empty? (If I define a function from A to B should I take care to ensure that A is non-empty?)

Prove that the group ring ZpG is not a domain. Homework Statement Let G be a finite group and let p >= 3 be a prime such that p | |G|. Prove that the group ring ZpG is not a domain. Hint: Think about the value of (g − 1)p in ZpG where g in G and where 1 = e in G is the identity element of...

Homework Statement I'm looking at integrals about the unit circle and need to show that they equal 0. integral[e^zdz/(z-2)] integral(sinz/zdz) integral[sinhz/(z^2+2z+2)dz] My thoughts on showing these is using series. Is this the right idea? Also I'm looking at a couple of...

If a function f is differentiable at a point x = c of its domain, then must it also be differentiable in some neighborhood of x = c?

Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance... For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain...

Hello, For spring break homework, I'm supposed to prove the Invariance of domain theorem (stating that continuous injective functions from an open set in R^n to R^n are open maps). Does anyone know of any books/sources of any kind which will help? Thanks!

Homework Statement How do you know whether you restrict the domain or range with a horizontal ellipse ? Homework Equations x^2/49 +y^2/10=1 The Attempt at a Solution

1. Let f(x)= 1/x where x is a rational number. What is the domain of f? Give a codomain and image for f that are not equal to each other. I am not sure about my answers, I got: D= (-infinity, 0) U (0, infinity) Image= (o, infinity) Codomain= Set of all reals I don't think this is...

Can you help me with this? I have a function with domain and range in R^2. What conditions it must have so that a point in the boundary of the domain will have its image in the boundary of the range? Thanks.

domain and range of the function help needed.. work shown! Given the function f(x)= (3x+4)/(5-2x) find the domain and range of the inverse function of f(x) work shown: it was proven to be one to one since f(x1)= f(x2) found inverse f(x) to be (5x-4)/(3+2x), i believe this is correct...

define the natural domain and range for f(x,y) = 1/sqrt(x^2-y) I get D= {(x,y)|x^2-y>0} same as saying y can not equal x^2 R= {(x,Y)|f>0} can someone tell me if I've approached this correctly?

Hello, This is the first time I'm using COMSOL on a problem where I have multiple subdomains within the domain. Previously, I have only been using one domain/one set of equations/Two global sets of BC's. I've been having a hard time thinking of a solution to my problem. I have 3...

Does Cramer's rule work in frequency domain? For example, if we have to solve two simeltaneous equations, as in nodel analysis or mesh-current method, can we use Cramer's rule to solve em? Would this be an efficient method?

Homework Statement I have a review in Calc and the question was: f(x) has a domain of [-1 , 5) Find the domain of g(x) = f(2x+3) Homework Equations The Attempt at a Solution I got [-1 , 2)

f(x)= x^(5/3) - 5x^(2/3) Need to find the domain of the above function? The graphing calculator shows x cannot be a negative number, and I don't see why not? Please help!

Domain Functions: f(x) = 4sq.root(1-x2), the 4 is on the outside f(s) = sq.root(s -1)/s-4 f(x) = x-4/sq.root x I have absolutely no clue how to go about doing any of these, I take notes but I cannot piece it together; I have never felt so helpless at anything. This isn't homework I...

Hi, I've been trying to understand more on frequency plots of images. 1. Assuming a 1d example of just a strip of an image; in the frequency map there are 'same' no. of frequencies as there are pixels. What is the reason for this? Does this have something to do with the Nyquist theorom...

Hi everybody, I have question: Why can you do Convolution filter in the frequency Domain ? I mean, when you apply a filter to an image in the spatial domain, it 's easy. You've got for example your sobel 3x3 kernel that you apply on every pixel of your image. Easy. But when you convert...

Whatever is a schlicht domain (complex analysis)? Laura

I've just discovered why my emails are bouncing back from particular friends. Those friends have AIM accounts (or similar), and it seems AOL (or other) has blacklisted my domain. A few months back my site was hacked and someone was using it for phishing. With the help of my ISP I've deleted...

This is more of a math question but i feel like i will get more help among Electrical Engineers. I successfully found the step response of an RC circuit in the time domain using Laplace Transforms. But i can't seem to figure out how to do it with an RLC transfer function. I have the following...

Does anyone have a textbook on multivariable complex analysis, and do they define a holomorphically convex domain in terms of the union of an ascending series of compact subsets? If so, how exactly does the definition go? Was it D=\bigcup K_n where K_n is holomorphically convex and compact...

Homework Statement Given a,b,c in D, with a not 0, we have ab=ac implies b=c. Show that the commutative ring D is an integral domain. The Attempt at a Solution I don't know where to begin with this.

Consider a simple alternating current generator such as Hippolyte Pixii's dynamo. The current generated by such dynamo can be described as simple oscillating cosine signal. Assuming for simplicity that the max current generated each time a pole of Pixii's magnet passed the coil is (2/pi)0.5...

How do you convert functions from the time domain, to the frequency domain For example: cos(250t + 30degrees) is what in the frequency domain? Are there some general steps I can follow to do this?

What is an empty relation? Can an empty relation be a function? Is an empty relation one with the empty set as its domain or as its range or both? THanks

I'm doing some exam revision and there's a few questions on finding the domain and range of functions of 2 variables. With a function of 1 variable I know that the domain and range is just finding the max and min x value, and the max and min y value. With a function of 2 variables I am...

Homework Statement Prove that the nonempty fibers of a map form a partition of the domain. The Attempt at a Solution Ok so we have some map phi: S -->T And we want to show that its pre-image phi-1(t) = {s in S | phi(s)=t} forms a partition of the domain. Im really confused here. I assume...

Homework Statement Show that R = {0.5(a+b(root2)) : a,b are integers} is not a domain [b]2. Homework Equations A commutative ring (non trivial) is a domain iff (ab=0 => a=0 or b=0) The Attempt at a Solution I've try to construct a counterexample where x, y in R and xy=0 but x,y=/=0...

Domain and range in ovals--what's this called? I was helping my friend with his math homework. He's in an intermediate algebra and is working on domains and ranges of functions. He came to me for help with this method of describing domains and ranges of functions using two ovals--one listing...

I just have a question which I'm confused about, this is the same right? Domain is (-∞,0) U (0,+∞) and Domain D: {XER, x ≠ 0} and this is the same right? Domain is (-∞,0) U (5,+∞) and Domain D: {XER, x ≠ 0, x≠ 5} Attempt : I know that U is used to...

Homework Statement Find a. (f+g)(x) b. (f-g)(x) c. (fg)(x) d. (f/g)(x) f(x)=2x-5 & g(x)=4 Homework Equations (f+g)(x)=2x-1 (f-g)(x)=2x-9 (fg)(x)=8x-20 (f/g)(x)=2x-5/4 The Attempt at a Solution When I've completed all the other equations, I'm stuck on domain. I'm thinking that its all...

hi this is my first time here. i have just been admitted to the university of the gambia last month. i have a problem with this question. please i need help find the domain f is such that x maps to 1 all over the squareroot of x2-10x+12.

We recall that Z is the set of all integers. For each i, j in Z, let f(i,j) be the larger of the two integers i and j. Do these remarks define a function? If so, what are the domain and the image? I'm not sure how to do this. I believe that the remarks do define the function. But I don't know...

Can you find an example of a simple domain not being skew field?

Why is the domain of arctan power series |x|<=1? i understand why a power series has the domain |x|<1, but why is the power series of arctan |x|<=1? thanks! also, why are domains of the taylor expansions of coshx and sinhx: for all x?

Write down the domain and range of the function g(x) = 1 / ((9 - x)2) Please enter your answer as a list [in brackets], using inequalities e.g. a domain (for x) of (-¥, 2) and a range (for g(x)) of (2, 5] may be entered as: [x < 2, 2 < g(x) and g(x) <= 5] I don't get it??

Homework Statement y= \frac{x + \frac{1}{x}+1}{x+\frac{1}{x}+2} That is equal to y = \frac{x^2+x+1}{(x+1)^2} Whenever I graph either one of those they are the same graph (as well they should be) and they have a value for x=0. But why should x = 0 be in the domain? And also if you go...

This is not for a specific problem, just in general: If we want to find the double integral of a function of two varaible, when we got other 1 varaible function to define the domain. What are the basics of drawing the domain in 2d (x, y only)?

Identify the domain and range for the function f= {(x,y) \in \mathbb{R} x \mathbb{R}:y=\chi _{\mathbb{Z}}(x)} f={(x,y)\in \mathbb{R} x \mathbb{R}:y=\frac{e^x + e^{-x}}{2} How do I determine the correct results. I am not really understanding the terminology.

Homework Statement y = \frac{1}{(x-1)(x+2)} find out the domain and range ans: y<= -4/9 or y>0 x~E~R~-\{-2,1\} The Attempt at a Solution I know the solution and I used this methoD: y(x^2 + x -2) =1 (where y\neq0 ) when x is real, the discriminant y^2...

Find the derivative. State the domain of the function and the domain of its derivative. f(x) = x + √x f(x) = (3 + x) / 1-3x Find F'(a) f(x) = (x^2 + 1) / (x - 2) f(x) = √3x + 1

I'm trying to find the wiki page (if it exists) on the domain-straightening theorem and the range-straightening theorem but searches for those words produce no results. I've also seen those theorems by the name of "canonical forms for submersion and immersion" (in Gallot-Lafontaine-Hullin)...

Hi! I have to integrate on a triangular domain \int_T f(x,y,z)dxdydz so I use simplex coordinates, i.e. x=(1-\alpha-\beta)x_1+\alpha x_2+\beta x_3 y=(1-\alpha-\beta)y_1+\alpha y_2+\beta y_3 z=(1-\alpha-\beta)z_1+\alpha z_2+\beta z_3 where (x_i,y_i,z_i) are the vertices of...

x = 2cot t y = (sin t)^2 t is greater than 0 but less than or equal to pi/2 The cartesian can be found using trig identities to be: y = 8/ (4+ x^2) What would be the range of the cartesian equation? I think it would be x is greater than or equal to 0, since when t = pi/2, x =...

The function f is defined by f(x) = ln(4 - 2x), x<2, and x is a real number write down the domain of the inverse. I know that the domain of the inverse is the range of the function, but I am puzzled as to what that would be! Would it just be any real number? Thanks

If f:\mathbb{R}^3\to\mathbb{R} is a continuous function, x_0\in\mathbb{R}^3 a fixed point, r>0 a fixed radius, and n\in\mathbb{R}^3 a fixed vector satisfying |n|=1, then is the equation \int\limits_{B(x_0 + \alpha n, r)} d^3x\; f(x) \;=\; \int\limits_{B(x_0, r)} d^3x\; f(x) \;+\...

Hi All, I have some problem about my Fortran program. When I execute my program, it says Run-time error M6201-MATH -atan2 : Domain error I don’t know what to do. Please help me out from this error. Thanks Logi

So...a cosine wave when shown in the frequency domain is represented by a 1/2 magnitude vector at the positive frequency and a 1/2 magnitude vector at the negative frequency. I am surprised by this because I cannot understand why a vector of magnitude 1 at the positive frequency of the cosine...