Divergence Definition and 776 Threads

\sum\frac{1*3*5 ... (2k-1)}{1*4*7 ... (3k-2)} from k=1 to infinity Does this series converge or diverge?? I have no idea where to begin, I don't understand it's format. Aren't series usually A+B+C ... but this is just multiplication ?! ? So ?? HELP!

Just for reference, i got this question from reading an online ebook: http://www.plasma.uu.se/CED/Book/EMFT_Book.pdf The bottom equation on page 24 is where i these equations came up. I have been reading some stuff and i keep coming across an annotation which looks exactly like a...

Hello I am trying to get my head around what the divergence actually represents physically. If you have some vector field v, and the components of v, vx, vy, vz have dimensions of kg/s ("flow" - mass of material per second) the divergence will have units of kg/(s*m) (mass per time distance)...

Homework Statement A vector field is defined by A=f(r)r a) show that f(r) = constant/r^3 if \nabla. A = 0 b) show that \nabla. A is always equal to zeroHomework Equations divergence and curl relationsThe Attempt at a Solution I tried using spherical co-ordinates to solve this. But I am not sure...

Homework Statement (x_n) is a sequence and x_1 > 2. From then on, x_{n+1} = x_n + 1/x_n Prove that (x_n) is divergent. Homework Equations n/a The Attempt at a Solution I first tried assuming that a limit existed, but I didn't get a contradiction. (I had x = 2 + 1/x, x = (2 \pm...

I just happened to read two papers that pretend that the quadratic divergence of the Higgs mass is not a problem. The first is "Vacuum energy: Quantum Hydrodynamics vs Quantum Gravity" http://arxiv.org/abs/gr-qc/0505104 (Update: this is now the correct paper from arxiv) where Volovik says that...

Homework Statement show that the definition of the invariant divergence divA = 1/√g ∂i (√g Ai) is equivalent to the other invariant definition divA = Ai;i Ai;k = ∂Ai/∂xk + ГiklAl Гkij = gkl/2 (∂gil/∂xj+∂glj/∂xi-∂gij/∂xl) Homework Equations g is the metric tensor...

Why is \nabla\cdot\vec{A}=\frac{1}{r}\frac{\partial}{\partial r}(rA_{r})+\frac{1}{r}\frac{\partial}{\partial \theta}(A_{\theta}) Where \vec{A}=A_{r}\hat{r}+A_{\theta}\hat{\theta} And \nabla=\hat{r}\frac{\partial}{\partial r}+\hat{\theta}\frac{1}{r}\frac{\partial}{\partial \theta} Instead of...

I've also posted this in the Math forum as it is math as well. --- I want to know if I'm on the right track here. I'm asked to prove the following. a) \nabla \cdot (\vec{A} \times \vec{B}) = \vec{B} \cdot (\nabla \times \vec{A}) - \vec{A} \cdot (\nabla \times \vec{B}) b) \nabla...

I've also posted this in the Physics forum as it applies to some physical aspects as well. --- I want to know if I'm on the right track here. I'm asked to prove the following. a) \nabla \cdot (\vec{A} \times \vec{B}) = \vec{B} \cdot (\nabla \times \vec{A}) - \vec{A} \cdot (\nabla \times...

Homework Statement Here is a link to the problem: http://www.brainmass.com/homework-help/physics/electromagnetic-theory/68800 The Attempt at a Solution To find the divergence 1/r^2*d(r)*(r^2*r^2*cos(theta)) +[1/r*sin(theta)]*d(theta)*(sin(theta)*r^2*cos(phi))...

What is the Divergence? is it only the Partial derivatives? Lets say I have a vector field: F=x^2i+y^2j+z^2k, the divergence is F=2xi+2yj+2zk? And if it is, than what is the gradient?:confused:

Hello, I was wondering if anyone could explain the troubling divergence here of the differential cross-section for rutherford scattering for \theta = 0. I know it must have something to do with the fact that the em force extends to infinity, which makes sense to me for the total cross section...

Homework Statement This is from my textbook Engineering Electromagnetics by John Buck and William Hayt 7th Edn, pg 238 in the chapter titled "The Steady Magnetic Field": Homework Equations Divergence theorem: \oint_S \textbf{B} \cdot d\textbf{S} = \int_{\mbox{vol}} \nabla \cdot...

http://img403.imageshack.us/img403/9478/roffelsw8.png I really can't understand the last sentence, how do they get that the sum has to be smaller than k/2?

Homework Statement Is the series from n=1 to infinity of 3/n converging or diverging? Homework EquationsThe Attempt at a Solution Since 3/n is not a geometric series, my guess is that we can just use the Test for Divergence and take it's limit to see if it's converging or diverging. As...

Dear friends, How is the divergence in curvilinear coordinates of a second order mixed tensor defined? I mean, shall I contract the covariant or the contravariant index?? And for both cases which is the physical meaning? \nabla_i N^i_j or \nabla_j N^i_j ? Thanks a lot, Enzo

"Helmholtz equation" Neumann and divergence Hello, I'm trying to solve the following elliptic problem : S = B - \mu\nabla^2 B Where S(x,y) and B(x,y) are 3 component vectors. I have \nabla\cdot S = 0 and I want B such that \nabla\cdot B = 0 everywhere. I'm using finite differences on a...

Does anyone know of any analytical expression for the upper bound on the Kullback–Leibler divergence for a discrete random variable? What I am looking for is the bound expressed as 0 <= S_KL <= f(k) Where k is the number of distinguishable outcomes. Ultimately I am also looking for...

Homework Statement The nth term for a sequence is the square root of [n/ (n^4 + 1)] Investigate whether it is convergence or divergence. Homework Equations Ratio test and integral test The Attempt at a Solution Ratio test will fail for this question, since no conclusion can be...

Homework Statement v = (a.r)r where r=xi+yj+zk and a is a constant vector show \nabla.v = 4(a.r) I let a= ai+bJ+ck then (a.r) = ax+by+cz then this (a.r)r = ax^{2}i+by^{2}j+cz^{2}k \nabla.v = da1/dx+da2/dz+da3/dz =2ax+2by+2cz which is equal to 2(a.r) am i wrong or the book?

I am slightly unsure about how the divergence can be increased by the use of either bi-concave or plano-concave lenses. I understand the general theory behind it but am having trouble putting numbers to it. e.g. if you have a laser beam with a diameter of 2mm and a divergence of 2mrad what...

Homework Statement Hi, I'm trying to follow the proof for the statement \nabla . u = 0 I'm basing it off this paper: http://delivery.acm.org/10.1145/1190000/1185730/p1-bridson.pdf?key1=1185730&key2=4151929021&coll=GUIDE&dl=GUIDE&CFID=25582973&CFTOKEN=82107744 (page 7, 8) In...

Homework Statement Suppose a_n > 0, s_n =a_1 + ... + a_n, and \sum a_n diverges, a) Prove that \sum \frac{a_n}{1+a_n} diverges. Homework Equations The Attempt at a Solution Comparison with a_n fails miserably.

As the thread title suggests, I'm having trouble realizing when the divergence theorem is applicable and when it is not. In some examples, I am instructed not to use it because it doesn't hold but on others I can use it. My first instinct was that it doesn't apply when the vector field isn't...

Homework Statement Lets say that I have some sequence (a_n) which converges to 0 at infinity and that for all n a_{n+1} < a_n but the sequence (a_n) diverges. Now I know that the series (cos(n) a_n) converges but can I use the following argument to prove that |cos(n) a_n| doesn't...

Homework Statement Well I am studying for my final which is in a couple of days, and I am stuck on this topic of convergence of improper integrals. I've been doing a couple and I thought I was doing them correctly but my answers do not go with the answers I was given. So I am stressing out...

Homework Statement Let \vec{F}=xyz\vec{i}+(y^{2}+1)\vec{j}+z^{3}\vec{k} And let S be the surface of the unit cube in the first octant. Evaluate the surface integral: \int\int_{S} \nabla\times \vec{F} \cdot \vec{n} dS using: a) The divergence theorem b) Stoke's theorem c)...

I need help identifying if it converges or diverges or conditionally converges. \Sigma(-1)^{k}\frac{(k+4)}{(k^{2}+k)} First I want to test for absolute convergence, and comparing this limit to 1/k I get that it diverges. Since it diverges, I need to test it now using the Alternating...

Homework Statement Let D be an area in R^3 and S be its surface. D fulfills the Divergence theorem. Let N be the unit normal on S and let the volume, V, be known. Let (\overline{x},\overline{y}, \overline{z}) coordinates of the centre of mass of D be known (and the density delta is...

[SOLVED] Divergence, nabla Homework Statement Given the vector, find the dot product. Homework Equations dot product of nabla and the vector is just partial derivative of each component. The Attempt at a Solution I'm trying to figure out if I can just leave out the...

Homework Statement Investigate the behavior (convergence or divergence) of \sum_n 1/(1+z^n) where z is complex. Homework Equations The Attempt at a Solution If the modulus of z is less than 1, it is not hard to show that the limit of the sequence is not 0 (it is actually not finite) and thus...

I've been reading up on these three recently, and wondered if anyone could confirm what I think they do. I'm not 100% I understand these. del (\bigtriangleup), when applied to a scalar, creates a vector with that scalar as each of the XYZ values. eg \bigtriangleup . x = (x,x,x)...

I have a few series which I'm having trouble proving whether they converge or diverge. I know the following tests for convergence: comparison test, ratio test, n-th term test, and root test. Here are the series and what I have tried so far: \sum n -1 / n2 : I'm assuming this series diverges...

Homework Statement Hi all. Please take a look at the following problem: Evaluate the surface integral \int{F \cdotp d\vec{S}} for the following vector field: F(x;y;z) = xyi + yzj + zxk, where i, j and k are unit vectors. S is the part of the paraboloid z = 4-x^2-y^2 that lies above the square...

Can anyone tell me whether or not the divergence theorem requires a conservative vector field? On a practice exam my professor gave a vector field that was nonconservative (I checked the curl) and proceeded to perform the divergence theorem to find the flux. On one of my homework problems I...

I want to calculate the divergence of a two dimensional 3 order tensor; e.g. nabla=(d/dx, d/dy) and Ax = ( C D) ( E F), Ay = ( G H) ( I J) (it's a 2x2x2 cube). Index notation: (nabla)_i = d/dx_i and elements of A are A_ijk How do I contract it properly...

[SOLVED] Beam Divergence Homework Statement A 1.5mW helium-neon laser beam delivers a spot of light 5mm in diameter across a room 15m wide. The beam radiates from a small circular area of diameter 0.5mm at the output mirror of the laser. Assume that the beam irradiance is constant across...

S\int\int F*Nds F(x,y,z) = (xy^2 + cosz)i + (x^2*y + sinz)j + e^(z)*k s: z = 1/2\sqrt{x^2 + y^2} , z = 8 divF = y^2 + x^2 +e^z Q\int\int\int (y^2 + x^2 + e^k)dV This is as far as I got, I have no idea how to do the limits for this triple integral thanks in advance guys.

When do I use the Test for Divergence. I am confused because on some problems I get that the limit of the equation is not equal to 0 and it is convergent. But using the Test for Divergence every answer I had in the other problems would be contrary to the answer I got which I know to be right. I...

Hello - I'm supposed to derive the divergence formula for spherical coordinates by carrying out the surface integrals of the surface of the volume in the figure (the figure is a piece of a sphere similar to a box but with curves). The radial coord is r. The polar angle is \varphi and the...

Homework Statement Determine whether the following integral is convergent or divergent. If convergent, what does it converge to? dx/(4x^2 + 4x + 5) [-infinity, infinity] Homework Equations comparison theorem?The Attempt at a Solution I think it is convergent, so I set the original integral...

Consider a cylindrical shell so that the cross sectional radius is some constant a. In the first term of the divergence expression in cylindrical coordinates: \frac{1}{r}\frac{\partial}{\partial r}(rA_{r}) When I multiply the radial component by r, do I go ahead and substitute r=a...

Hello everyone, I'm new to this forum. I have a doubt about differential forms, related to the divergence. On a website I read this: "In general, it is true that in R^3 the operation of d on a differential 0-form gives the gradient of that differential 0-form, that on a differential 1-form...

Homework Statement Can someone please explain to me what the physical meaning of the divergence integrals and curl integral is? In the problems I have come across, they ask us to calculate areas and etc.. using Green's theorem. Which one should I use in that case? Thank-you very much for...

Suppose that a_n\geq 0 and there is \lim_{n\rightarrow\infty}\frac{a_{n+1}}{a_n}=c If c>1,series diverges. if c<1 series converges. For a_n=\frac{n!}{n^n} \lim_{n\rightarrow\infty}\frac{(n+1)!/(n+1)^{n+1}}{n!/n^n} \lim_{n\rightarrow\infty}\frac{n^n}{(n+1)^n} Then I used...

The sum of 1-2+3-4+5..., and divergence The sum of 1-2+3-4+5..., which can be written as Diverges for m = infinity, yet there are postulates that this is equal to \frac{1}{4}. First, I don't understand how you can obtain a fraction out of a natural numbers if they are consecutively...

Homework Statement Show divergence theorem works For the vector field E = \hat{r}10e^{-r}-\hat{z}3z Homework Equations \int_{v}\nabla \cdot E dv = \oint_{s} E \cdot ds The Attempt at a Solution \nabla \cdot E = 1/r \frac{d}{dr}(rAr)+1/r\frac{dA\phi}{d\phi}+\frac{dAz}{dz}...

I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does. \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and...

Homework Statement Determine whether the following sequence, whose nth term is given, converges or diverges. Find the limit of each convergent one. n[1 - cos(2/n)] Homework Equations I have made a solid attempt and obtained an answer but I am convinced I made a mistake and have missed...