Domain Definition and 743 Threads

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!

Hi all, The problem at hand is a bubbly flow in a cylinder: I'm using an FEM to identify how the walls effect the drag on bubbles in a flow. To test my results I want to set up an infinite cylinder with randomly distributed spheres and then average the Navier-Stokes equations over the entire...

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!

Homework Statement I have to develop an algorithm that can predict dominant peaks in the frequency domain, given a set of data in the time domain. I used FFT to check the frequency domain but apparently there are packet losses and irregular sampling intervals so FFT won't work. 2. The...

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} +...

Homework Statement I need to find the domain of absolute convergence of the following series: ^{\infty}_{1}\sum(z+3)^{2n}/(2n)! Homework Equations Ratio test? The Attempt at a Solution I'm not really sure how to handle the complex variable z within the series. I attempted to use the...

Homework Statement Suppose that the function f is defined on an interval by the formula f(x) = \sqrt{tan^{2}x - 1}. If f is continuous, which of the following intervals could be its domain? (A) (\frac{3\pi}{4},\pi) (B) ( \frac{\pi}{4},\frac{\pi}{2} ) (C) ( \frac{\pi}{4},\frac{3\pi}{4}...

Homework Statement Find the domain and range: { x+2, x\leq0 f(x) ={x3, |x|<1 {-x+3, x\geq1 Homework Equations domain = possible inputs range = possible outputs The Attempt at a Solution domain of f(x) = (-\alpha, -1] \cup (-1, 1) \cup [1, \alpha)...

I have a question about domain. Let's say we have a function in the form of y=(C/X)^0.5 Let's say for a particular case C = 0. Is the domain of the function x cannot equal 0? Or is it all real?

f(x) = -√(t(1-t)) Domain: 0≤t≥1 (from Null Factor law) Range: 0≤t However, the range was wrong. The answers said that it was -0.5≤t≥0. I have no idea where the -0.5 came from. I substituted the domain values in but i didn't work. It just came out with zero. Can anyone suggest any ideas...

Show that if R is an integral domain with characteristic p>0, then for all a,b in R, we must have (a+b)^p=a^p+b^p. Show by induction that we must also have (a+b)^p^n=a^p^n+b^p^n for all positive integers n. R is an integral domain, so ab=0 implies a=0 or b=0. The smallest positive integer...

Consider the mapping f: X\rightarrowY where f(x)=y=\sqrt{1-x^2} consider the co-domain Y , we can define the mapping over [-1,1] \rightarrow \mathbb R , ( in this case the mapping won't be onto) and in case we define the mapping over [-1,1] \rightarrow [0,1] (in this case mapping is onto) (is...

Greetings to all. :smile: I have 2 simple questions, one is simply a confirming the answer query, and the other is domain related (like topic title says). 1) In this question, we are asked to show that a2+b2 is constant for all values of \theta. We have a and b as...

Homework Statement My domain i numbers of form 4k+1. n divides m is this domain if n=mk for some k in the domain. A number is prime in this domain if its only divisors are 1 and itself. My problem is to find a number in the domain with multiple prime factorizations. Homework Equations...

Boundary conditions & time domain electromagnetic waves: does classical model fit? Consider two propagating media: a lossy dielectric medium and a lossless dielectric medium. Thus, the interface that separates them has two tangential components of electric field, one for each medium. One of...

Homework Statement Let R be a ring with no zero divisors such that for any r,s\in R, there exist a,b \in R such that ar+bs=0. Prove: R=K \oplus L implies K=0 or L=0. Homework Equations Definition of direct sum of modules, integral domain... The Attempt at a Solution I didn't know...

Homework Statement I don't have a real question, i was looking for where i could find info on the domain of influence, regarding pdes Homework Equations The Attempt at a Solution

Homework Statement determine the char. curve and gen. sol. for x^{3} \frac{\partial{u}}{\partial{x}} - \frac{\partial{u}}{\partial{y}} = 0 Homework Equations find sol and domain of influence when u(x,0) = \frac{1}{1+x^2} show sol is not defined...

hello, i am new here and this is my first post so please bear with me for any mistakes or so.. now my question is about time domain analysis and frequency domain analysis . why should one convert from time domain into frequency domain by using Fourier transform ? and what are...

Homework Statement Let p be a prime number, and let D = {m/n| m,n are integers such that p does not divide n} Verify that D is an integral domain and find Q(D) Homework Equations i am unsure where to use the fact that a prime number divides n in this proof. I know how to check that D is an...

Homework Statement In exercises 39-46, f refers to the function with domain [0,2] and range [0,1], whose graph is shown in Figure P.55 (how do I draw and paste graphs? the graph looks like an upside down curve with a maximum height or range of (1,1) and a width or domain of (0,2)). Sketch...

let a function f: A -> R^m where A is a subset of R^n. if a is an accumulation point of the domain of f, the set A, then f(A) is an accumulation point of the set R^m. i'm not sure if this statement is true or not but if it is, how would I prove this result? i was thinking of using the fact...

Homework Statement Let R be an integral domain with identity element 1. Show that there at most two elements "a" in R such that a^2=1 Homework Equations The Attempt at a Solution Being an integral domain implies that if ab=0, then a=0 or b=0. a^2=1 implies a=1. Then (a)(a) =...

Homework Statement f(x) = x^3/(x^2+ 1) 1. Identify Domain and Range 2. x and y intercepts (if any) 3. local and global extrema 4. Equations of the asymptotes (if any) Homework Equations f(x) = x^3/(x^2+ 1) The Attempt at a Solution f(x) = x^3/(x^2+ 1) f'(x)...

I am trying to find the domain of this function f(x)=sqrt(x^2 - 2x +5). i am supposing that y=x^2 - 2x +5 and y must be greater of equal to 0. in otherwords where the graph is touching or above x axis. to find where the graph is touching x-axis i am trying to find the x intercept and i get...

Homework Statement F(x) \ = \ \int\limits_{1}^{x^2}{\frac{10}{2+t^3}} \ dt Where {0}\leq{t}\leq{4}. Find the domain of F. Homework Equations N/A The Attempt at a Solution I'm not quite sure how to tackle this problem. It doesn't seem as though the domain of t has much at all to do with...

Domain of f(x,g(x)), and partial derivatives Watching http://www.khanacademy.org/video/exact-equations-intuition-1--proofy?playlist=Differential%20Equations Khan Academy video on exact equations, I got to wondering: if x is a real number, what is the domain of a function defined by f(x,g(x))...

Hi everyone! I started studying differential equations, but I still didn't understand why the domain of the solutions must be defined in an interval. For example the solution of the following initial value problem: \frac{dy}{dt} + \frac{1}{t}y=0,y(1)=1 is given by y(t)=1/t that has it's...

how would wavefrom change change in time domain, frequency domain and its rms value if a dc level of 1 volt was added.

Homework Statement Put the following rings in the smallest class: a. Z b.Z5 c. Q d. Z5[x] e. Z[i] f. Z[\sqrt{}-5] g. Z[x] h. Q[x] Homework Equations four class are euclidean \subset principal ideal \subset unique factorization \subset integral The Attempt at a Solution What I got...

I have read a lot of paper about fatigue damage, in some fields it is particularly used the time domain approach while in others the frequency domain approach, but I haven't understood when it is better to use frequency approach respect time domain approach. May you help me to understand better...

Question: Show that if R is an integral domain then R^x=R[x]^x(or that the units in R[x] are precisely the units in R, but viewed as constant polynomials).