Domain Definition and 704 Threads

Hey guys, So I'm trying to intuitively understand the conclusion that a contraction in one domain leads to an expansion in the other domain (and vice-versa). Mathematically, I can see how this would happen, e.g., a bandpass filter with -pi/2 < w < pi/2 would result in a narrower time domain...

Hi guys! I'm to find the solution to \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} Subject to an initial condition u(x,0) = u_0(x) = a \exp(- \frac{x^2}{2c^2}) And Neumann boundary conditions \frac{\partial u}{\partial x} (-1,t) = \frac{\partial...

Homework Statement Let W be the region between the paraboloids z = x^2 + y^2 and z = 8 - x^2 - y^2 Homework Equations The Attempt at a Solution for each domain, 0 ≤ z ≤ 8 0 ≤ r ≤ 2 0 ≤ θ ≤ 2\pi So... \int^{2\pi}_{0}\int^{2}_{0}(8-2r^{2})r drdθ

1. The problem statement, all variables and given known data f(x,y,z,) = e^{2x-z} W: x + y + z ≤ 1 x, y, z ≥ 0 Homework Equations The Attempt at a Solution For each domain, could you check it please? This is the only triple integral that's haunting me 0 ≤ x ≤ 1-y-z 0 ≤ y ≤...

Homework Statement f(x,y,z) = 1 x^{2} + y^{2} + z^{2} ≤ 4z z ≥ \sqrt{x^2 + y^2} Homework Equations The Attempt at a Solution How can I know ρ if there is z variable? Do I just square root both 4 and z? For θ, since it is sphere it would be 0 ≤ θ ≤ 2\pi right? for \phi, is...

Homework Statement f(x,y) = (x^{2} + y^{2})^-2 x^{2} + y^{2} ≤ 2 x ≥ 1 Homework Equations The Attempt at a Solution -4\pi ≤ θ ≤ 4\pi secθ ≤ r ≤\sqrt{2} are these the correct domain?

Homework Statement f(x,y) = e^{x^2+y^2} x^{2} + y^{2} ≤ R Homework Equations The Attempt at a Solution I believe this is a circle. f^{2pi}_{0}^{sqrt(R)}_{-sqrt(R)}e^{x^2+y^2}*r*dr*dθ = f^{2pi}_{0}f^{sqrt(R)}_{-sqrt(R)}e^{r^2}*r*dr*dθ after u substitution... =...

Homework Statement f(x,y) = y(x^{2} + y^{2})^-1 y ≥ \frac{1}{2}, x^{2} + y^{2} ≤ 1Homework Equations The Attempt at a Solution Would you check my domain please? f^{pi}_{0}f^{sqrt(3)/2}_{-sqrt(3)/2} sinθ drdθ

I am studying Control Theory from Ogata. My math is a little rusty, so this is a math question about Frequency Domain Analysis. Check this page - http://www.flickr.com/photos/66943862@N06/6337116280/sizes/l/in/photostream/ I get everything upto Equation 8-4 However I don't get the line after...

Homework Statement Question as in image: Homework Equations The Attempt at a Solution When I did Mesh, I got this: -20j-20Ia+(Ia-Ib)2j=0 (Ib-Ia)2j-(Ib-5)j-(Ib-Ic)50=0 -(Ic-Ib)50-(Ic-5)8j-2(Ia-Ib)=0 2(Ia-Ib)-100Id=0 Ia-Ib=Ix **This is done from Left to Right**...

Homework Statement f(x)=sin(2x+5) Homework Equations I am supposed to find the derivative, and the domain of it. The problem is that I cannot deal with the simplification of it. The Attempt at a Solution As far as I know, I am suppsosed to use f(x+h)-f(x)/h =...

Hi, I stumbled upon the following two functions which have the same freq domain representation, 1/(j.pi.f) 1.signum(t) = u(t) - u(-t) 2. 2u(t) what is the reasoning behind them having the same f domain representation?

In an example in my algebra text, (from the section on unique factorization domains) it is describing the ring \mathbb{Z}[\sqrt{-5}], and demonstrating that it is not a UFD. It starts by giving the norm N(a+\sqrt{-5}b)=a^2+5b^2. It remarks that if zw=1, then N(z)N(w)=1, and then it goes on...

The first hypothesis is that f is continuous on [a,b]... Is there a more concise mathematical way of saying... "because the function f is a polynomial it is continuous in its domain."? Because I rather not write that on my test it looks sloppy and non professional...

Hi everybody, i am having difficulties to write a program using only MATLAB to solve the Mrtd SCHEME...that is solving the maxwell equations...can anyone please help me

Hi just a quick question Differentiate f and find the domain of f. (Enter the domain in interval notation.) f(x)=(1/(3+lnx)) Here is my Derive: ((-3+lnx)^-2)(1/x) which is correct And for the domain (web assign wants interval notation) When I was doing this part, I wasn't sure if it...

"Positive Set" in an Ordered Integral Domain I'm currently reading Durbin's Modern Algebra, and I have a question about the positive set in ordered integral domains. Durbin characterizes an ordere integral domain as one with a subset which is closed to addition and multiplication, and...

Homework Statement We have to find the domain range (hope I'm using this right) of some functions, one of them being h(x)=f(x)^g(x), say h(x)=(x^2-4)^(x). I've been looking around and couldn't find the domain range of the x^x function, so I am kinda stuck on this one. Homework Equations...

Homework Statement I don't remember the exact question right now, but it was something like this: f(x) = sqrt(4 - x^2) I needed to give the domain / range of it, and also symmetry I believe. Homework Equations The Attempt at a Solution I know this is a half circle after...

Homework Statement I started out with f(x)=sinx and g(x)=1-√x. I found f(g(x)) which is sin(1-√x) and now my problem is how to find the domain. I've really been struggling with the domain part and just need this one done step by step so i have an idea of how to actually do it. Homework...

Homework Statement 1. Rewrite as piecewise: g(x) = 2x - |3x-2| 2. Give domain and equation represented by f(g(x)) when g(x) = √(x+1) and f(x) = 3/x 3. Give range of P(x) = {2x-1, x >/= 1 {x^2 + 1, -1 </= x < 1 {√|x|, x<-1 thanks in advance Homework Equations The Attempt at...

Homework Statement Discrete-time transforms What does it mean when it says this : These transforms have a continuous frequency domain: Discrete-time Fourier transform Z-transform What is the meaning of continuous frequency domain..?

Apparently, when convolving, for example: [δ(ω-π) - δ(ω+π)] * (δ(ω+50π)-δ(ω-50π)) the result is δ(ω+49π)-δ(ω-51π)-δ(ω+51π)+δ(ω-49π) where δ() is the Dirac delta function, * the convolution operator and ω the frequency variable How do we get to this? Can you help me on the intuition in...

Hi, I am new to signal theory and don't know what is time domaine signal and frequency domaine signal. Please some can explaine me clearly and how can we convert between those two domaines. I read the topic in wikipedia which makes me somepart clear but interested to know...

So I'm having trouble understanding how these two are related, i.e., how one proves the other. I understand the ideas behind both of them: For J-B, you're basically taking R^n and throwing in a sphere, so the inside of the sphere is bounded and everything outside the sphere is unbounded. For...

What is the "domain of a die"? - Haim Permuter: Mathematical methods in communication: http://www.ee.bgu.ac.il/~it09/lec1/lec1.pdf (PDF notes). What is the domain of X, and what is its rule? Is the domain the set of ideas {the concept of the die landing on 1,...,the concept of the die...

In an integral domain, I found that the number of maximal ideals in a Notherian ring containing a particular element is finite. If the condition is dropped that the ring be Notherian, can anything like this be said?

I found the unity to be 1. I'm not sure how to determine 3) for each. http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110805_224110.jpg?t=1312602377 http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110805_224012.jpg?t=1312602392

Hey @ all, when windowing in DSP in time domain one multiplies all recorded time samples with a weighting factor (hanning, hamming, etc.), followed by a Fourier transform (FFT) to reduce sidelobes in the spectral domain. But now when thinking about starting up in frequency domain where I...

Homework Statement Hello. Can someon help me understand the difference between these two problems? #1: f(x)+3 #2: f(x+3) The reason I want to know if becuase my question tells me to use the domain of f(x) as [4, 8] and the range as [2, 6] Then it wants to know the domain and range...

Hi all, I have a filter whose amplitude and phase response in terms of w(omega) is known to me which i calculated numerically. Hence, the value is known only for discrete values of w(omega). Now, I want to know the output which this filter will produce on sending a temporal pulse(pulse in...

In many cfd textbooks the domain of dependence is stated as the entire region emclosed by the characteristics. Is this correct? Isnt it only the values on the characteristics? Thanks!

Hello PF members I am a very new member to your forum and very new to time-frequency transformation. Over the summer I will be doing some research on vibration signals and for now I want to start understanding some basic things upon the time and frequency domain and transformation...

Homework Statement a metal box with square base a no top holds 1000 cubic centimeters. it is formed by folding up the sides of the flattened pattern picture and seaming up the four sides. the material for the box costs $1.00 per square meter and the cost to seam the sides is 5 cents per meter...

I'm working on a high power multi-phase DC/DC converter where the load current has some fast transients. We can easily measure the output voltage in the time domain, and also measure the power distribution network impedance in the frequency domain. So, I think I would try converting the...

This question is at the end of a section on the Intermediate Value Theorem in my Real Analysis notes: Find a continuous function f: [-1,1]->R which is one-to-one when restricted to rational numbers in [-1,1] but is not one-to-one on the whole interval [-1,1] I can't figure it out. I've...

Homework Statement Let c and d be two non-zero elements of a domain D. If a and b are integers s.t gcd(a,b)=1, a>0, b > 0. If we know c^a=d^a and c^b=d^b, does it follow that c=d? Homework Equations The Attempt at a Solution I'm thinking divinding the two might be...

Homework Statement Let log z be the principal branch of the logarithm function defined −pi < arg z < pi the domain to define f(z)=loglog z?? Homework Equations The Attempt at a Solution I already know how to represent the arg z by arctanb/a+2pi*k how can I get arctan [Re (log...

I'm private studying a section in Linear Algebra first dealing with complex numbers. Now, I am ok with most of the answers, but I need help particularly with where this function is differentiable. Homework Statement Let f(z) = ln|z| + i arg z, 0<=arg z<2pi. What is the domain? What is...

Homework Statement Show how to determine the domain of each of the following functions: a) f(x) = ln(1 - ln(x)) b) g(x)=(x^2 -1)/(x^4・e^2x - 2x^2・e^2x - 8e^2x) c) h(x)= sqrt(6-e^-5t) Can somebody show me how to do these questions? Homework Equations The Attempt at a Solution I...

Hey guys, I am stuck trying to create a function in matlab... x[n] = {1 0 =< n =< 4 {0 elsewhere so far I have this... n = [0:4]; x[n] = 1; but I get this error: ? x[n] = 1; | Error: Unbalanced or unexpected parenthesis or bracket. and I can't figure...

hello,everyone,I'm from Shanghai, china.I got a problem when i was reading papers.I can't understand what is the partial derivative of a domain.I suppose it may be a curve,but exactly which curve it is? thank you very much!

I'm doing LaPlace transforms for a circuits class, and I realized that I don't REALLY know what the S domain is. When you do Fourier transforms, obviously you're in the frequency domain and that's pretty easy to understand. The other domain you work in a lot is time. But up until now, I've just...

So you see it all over the place, \mathbb{Q}(\sqrt{-5}) is not a UFD by finding an element such that it has two distinct prime factorizations...but what about showing that \mathbb{Q}(\sqrt{5}) is a UFD? I'm only concerned with this particular example, I might have questions later on regarding a...

Homework Statement Give an example of a commutative ring R with a 1 and nonzero prime ideal P of R such that P = P2 Homework Equations The Attempt at a Solution Letting R be an integral domain and look at the ideal 0xR in RxR. is all i got but not sure how to show this or what to...

For finding domain of a function in Rn, I have jot down some of the points. Assuming, if one or more of these 'x'es are a part of the expression of a function f(x1, x2, x3,…, xn), we do the following in writing down the domain: - for √x we write x≥0 - for 1/x we write x≠0 - for 1/√x we...

Homework Statement Sketch the z-plane pole zero diagram for: G(z) = \frac{z^{2} + z + 1}{z^{3}} Also sketch the time and frequency domain repsonses, the latter in amplitude and phase. Homework Equations G(z) = \frac{Y(z)}{X(z)} Zeros when Y(z) = 0; Poles when X(z) = 0 For...

I'm having trouble following a step in my notes: first off the heat equation is given by: \frac{\partial u}{\partial t}=k^{2}\frac{\partial^{2}u}{\partial x^{2}} then take the Fourier transform of this w.r.t.x, where in this notation the Ftransform of u(x,t) is denoted by U(alpha,t)...

Homework Statement y= -4(√4x-1) -1 in case it's not clear, the 4x-1 part is all under the radical the question is to graph and find the domain and range Homework Equations The Attempt at a Solution This is probably what your supposed to do , but not sure, OK To get the domain set everything...

Homework Statement Let f(z) be analytic on a domain D. Let \Delta = (\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}) Set W = |f(z)|2 show that W\DeltaW = (Wx)2+(Wy)2Homework Equations The Attempt at a Solution W = (U2+V2) \DeltaW = (\frac{\partial^2}{\partial x^2} +...