Divergence Definition and 775 Threads

Homework Statement Show that the vector v = \frac{\hat{r}}{r2} (not sure why formatting isn't working?) v = (r-hat) over (r squared) has zero divergence (it is solenoidal) and zero curl (it is irrotational) for r not equal to 0 Homework Equations div(V) = (d/dx)V_x + (d/dy)V_y +...

Please teach me this: It seem that the ultraviolet divergence has origin of we unknow the physics at very small distance(very large momentum,then very small distance).So we must cut off the very large momentum by renormalization procedure.But I do not understand the origin of infrared...

Hi everyone! I'm having a lillle problem proving that the einstein tensor is divergence free! I don't know how to begin, i start with \nabla_\mu G^{\mu\nu}=\nabla_{\mu}(R^ {\mu\nu} -\frac{1}{2}g^{\mu\nu}R) i tried to do \nabla_\mu...

I took the divergence of the function 1/r2\widehat{r} in spherical coordinate system and immediately got the answer as zero, but when I do it in cartesian coordiantes I get the answer as 5/r3. for \widehat{r} I used (xi+yj+zk)/(x2+y2+z2)1/2 what am i missing?

I noted that if [itex]f : C \to C[\itex] is holomorphic in a subset [itex]D \in C[\itex], then [itex]\nabla \by \hat{f} = 0, \nabla \dot \hat{f} = 0[\itex]. Moreover, those two expressions are equivalent to the Cauchy-Riemann equations. I'm rewriting this in plaintext, in case latex doesn't...

Hello, I have a problem with divergence function DIV in DERIVE 6 and canot find anything in help and web forums either. #1. At first, I load utility "VectorMatrixFunctions.mth" #2. when I insert DIV([1/r^2, 0, 0], spherical) I obtain ZERO But it seems wrong, f.e. for Gravitation we...

Homework Statement A 50W lamp radiates isotropically and has a spectral width of 750 nm and a centre frequency of 600 nm. How much of its total output power is emitted into a solid angle of 10^-6 Sr? What is the diameter of the spot that a beam subtending this solid angle makes on a...

Let's assume that a compact Lie group and left invariant vector filed X are given. I wonder why the divergence (with respect to Haar measure) of this field has to be equall 0. I found such result in one paper but I don't know how to prove it. Any suggestions?

I have 4 problems left and the questions says I have to test them for converge or divergence. Here are the problems http://gyazo.com/f0fa5a38c5968ecb7e74103486a181bd.png http://gyazo.com/4689f9d02d0b264c2c2b64ff4907ba77.png for 25, I want to take the limit as n goes to infinity however I get...

Homework Statement Homework Equations The Attempt at a Solution I can get the answer after applying divergence theorem to have a volume integral. But how about about the surface integral? It seems the 4 points given can't form a surface.

For there to be curl is some vector field fxy cannot equal fyx. Where fx= P, and fy=Q. Since the (partial of Q with respect to x)-(Partial of P with respect to y) is a non zero quantity giving curl. I understand that the terms will cancel due to the right-handedness of the definition but we...

Homework Statement given an = ( -1 )(n+1) / \sqrt{n} determine if the infinite series is Absolutely Convergent, Conditionally Convergent, or Divergent. Homework Equations I hope I have these theorems down correctly, please correct me if I'm wrong. If \Sigma|an| is Convergent then...

Homework Statement Decide whether the series below is absolutely convergent, conditionally convergent, or divergent: \sum_{1}^{\infty}(2n+3)!/(n!)^2 The Attempt at a Solution By graphing the equation, I am confident that the series is divergent, but I don't know how to prove it. I...

Anybody know Einstein notation for divergence and curl? What I would like to do is give each of these formulas in three forms, and then ask a fairly simple question; What is the Einstein notation for each of these formulas? The unit vectors, in matrix notation...

I've been having some trouble understanding how to determine if a sequence is divergent or convergent. For example an = cos(2/n) I know if I take the limit as n ->\infty then I will get 1. So the sequence has a limit but does having a limit mean that the sequence is convergent.

Hi, Say you want to use a proof by contradiction to prove that a sequence diverges. So you assume that x(n)-----> L , and try to find a real number, call it M, such that |x(n) - L| can never get smaller than M, thus arriving at a contradiction. My question is: can M be of the form that...

I'm reading gravitation and having trouble with one of the exercises. aRab+bRgab is the general tensor the exercise asks to show that the divergence of this tensor vanishes if and only if b=-1/2a how do I go about solving this problem?

the divergence and the curl of a vector field "A" are specified everywhere in a volume V. The normal component of curl A is also specified on the surface S bounding V. Show that these data enable one to determine the vector field in the region

http://scienceblogs.com/principles/2010/02/physics_quiz_accelerated_twins.php The answer, they claim, is that Alice ages more than Bob. But say this were true, it would also mean that of two synchronized clocks placed on opposite sides of the earth, one at sunrise, and the other at sunset...

Divergence and Curl in cylindrical and spherical co are: \nabla \cdot \vec E \;=\; \frac 1 r \frac {\partial r E_r}{\partial r} + \frac 1 r \frac {\partial E_{\phi}}{\partial \phi} + \frac {\partial E_z}{\partial z} \;=\; \frac 1 {R^2} \frac {\partial R^2 E_R}{\partial R} + \frac 1 {R\;sin...

[b]1.The problem asks " use the divergence theorem to evaluate the surface integral \int\int F.ds for F(x,y,z) = <x3y,x2y2,−x2yz> where S is the solid bounded by the hyperboloid x^2 + y^2 - z^2 =1 and the planes z = -2 and z=2. i know that the \int\int F.ds = \int\int\int divFdv...

i need to prove that div(R/r^3) = 4πδ where R is a vector and r is the magnitude of the vector R. also δ is the dirac delta function. so div(R/r^3) is 0 everywhere except for the origin. i need to show that the volume integral of div(R/r^3) = 4π as well. using the divergence theorem we...

Not really a homework problem, just me wondering about this: why is there a problem here? Say you want to use the divergence theorem in conjunction with Stokes' theorem. So, from Stokes' you know: Line integral (F*T ds)= Surface integral (curl(F)*n)dS. And you know that Surface...

can anybody tell me the expansion for the divergence of tensor vector product \nabla.(\tilde{K}.\vec{b}) for the case of scalar and vector the expansion is given by \nabla.(a\vec{b})=a\nabla.\vec{b}+\vec{b}.\nabla a

In which geometry of physical system the \nabla.\overline{J} ie divergence of J is zero? How does the Maxwell equations turns out?

I am not able to find any good reference to answer my question, so I will post here how does divergence theorem translates to 4 dimensional curved spacetime. I understood how volume integral changes but I am not able to understand how surface integral changes. I will be glad if some one...

Homework Equations Hey guys I had a slight problem trying to find divergence of vector fields for the following equation: F(x,y,z)=(yzi-xzj-xyk)/(x^2 + y^2 + z^2) So I want to know if its possible of substitute (x^2 + y^2 + z^2) for 1 since that is the equation of a sphere? If not...

If F is a well defined vector field and divF=0 then does that mean the flux of F across any surface in 3D would also be 0? I know that in divergence theorem, divF=0 automatically implies that the integral will be 0 but what about across flat surfaces and planes?

Homework Statement Yeah I've been pondering over that, my book doesn't really do the justice of nailing it down for me. Does having 0 divergence means having "absolute convergence", like maybe at every point (or at a certain point) all the vectors are pointing towards a point? Like...

Absolute Convergence, Conditional Convergence or divergence... Homework Statement \sum_{n=1}^{\infty} \frac {(-2)^{n}}{n^{n}} Homework Equations \lim_{n \rightarrow \infty} | \frac {a_{n+1}}{a_n}| < 1 \;\; absolute\; convergence \lim_{n \rightarrow \infty} | \frac...

Evaluate http://webwork.latech.edu/webwork2_files/tmp/equations/93/91cfe28c766cad38444f0213c651281.png where http://webwork.latech.edu/webwork2_files/tmp/equations/59/a56001472f977192637ea927c607a61.png and is the surface of the sphere of radius 6 centered at the origin. Ok so I started by...

Homework Statement Verify the divergence theorem for F(x,y,z) = (x,y,2z^2) and T is the region bounded by the paraboloid z=x^2+y^2 and the plane z=1. Homework Equations F(ds) = div(F)dV The Attempt at a Solution I have successfully evaluated the integral and come up with an...

Homework Statement My professor warned us that a few proofs will be on the finals. This could be one of them. However, we did a proof in class where he listed out a bunch of terms and then did an inequality to say it is divergent. I personally hated that long proof. I don't want to...

Homework Statement F(x,y,z) = (2x-z) i + x2y j + xz2 k and the volume is defined by [0,0,0] and [1,1,1]. Homework Equations flux integral = \int\int\int div F dV The Attempt at a Solution \int\int\int div F dV = \int\int\int (2+x2-2xz)dxdydz = 2 + 1/3 - 1/2 = 11/12 But I...

Homework Statement Evaluate the double integral over M (F \circ dS) where M is the surface of the sphere of radius 3 centered around the origin. (Sorry! I couldn't figure out how to use math symbols!) Homework Equations double integral(F\bulletdS)=triple integral (\nabla\bullet F)dV due...

Hello Friends, I am at a loss to understand a proof concerning the proof of divergence of (-1) ^n sequence. According to the book: "To prove analytically that the sequence is convergent, it must satisfy both of the following conditions: A: |-1-L| < epsilon B: |+1 - L| < epsilon " (+1...

i don't really understand the difference :( ∇2V versus ∇ (∇ . V) ? can anyone give me a simple example to showcase the application difference? thanks!

Let W be the solid bounded by the paraboloid x = y^2 + z^2 and the plane x = 16. Let = 3xi + yj + zk a. Let S1 be the paraboloid surface oriented in the negative x direction. Find the flux of the vector field through the surface S1. b. Let S be the closed boundary of W. Use the Divergence...

Homework Statement Determine whether the series is absolutely convergent, conditionally convergent, or divergent. \sum (-1)^n\frac{e^{1/n}}{n^4} Homework Equations The Attempt at a Solution I used the root test so \sqrt[n]{\frac{e^{1/n}}{n^4}} --> \lim_{n\to \infty...

Homework Statement Determine if the series the summation form n=2 to infinity of n/((n2+1)ln(n2+1)) is convergent or divergent. Homework Equations The Attempt at a Solution I applied the integral test and got positive infinity, so I it diverges. But I want to know if I'm right...

Homework Statement Is \sum(-1)^(n-1)*arcsin(1/n) absolutely convergent, conditionally convergent, or divergent? 2. The attempt at a solution The original function is alternating, so by the alternating series test, the function is convergent, because 0 < arcsin(1/(n+1)) <arcsin(1/n)...

Homework Statement what is the divergence of <y,z,x>? Homework Equations The Attempt at a Solution is the answer 0? seems too easy, lol, because the actual question is "compute the surface integral for F dot prod dS over domain T where T is the unit sphere and F = <y,z,x>"...

Please teach me this: Why the naively divergence of a diagram is ln(lambda) (where lambda is ultraviolet cutoff) when the superficial degree of divergence D=0(the divergence of lambda^D when D=0)).I am reading the renormalization theory in Schroeder&Peskin and I do not understand this.I do know...

Homework Statement For example in electromagnetism and I think it's true for any vector field, the relation \vec \nabla \cdot (\vec \nabla \times \vec E)=0. As far as I know, the curl of a vector field is a vector. So basically the above expression takes the divergence of a vector? It...

Homework Statement This problem I have been set is to find real life applications of divergence theorem. I have to show the equivalence between the integral and differential forms of conservation laws using it. 2. The attempt at a solution I have used div theorem to show the equivalence...

Homework Statement \Sigma from n=0 to infinity (-10)n/n! Determine the absolute convergence, convergence, or divergence of the series. Homework Equations In this section, it's suggested that we use the following to determine a solution: A series is called absolutely convergent if the series...

Homework Statement Hi, i am trying to find the div and curl in spherical polar coordinates for the vector field, F I have attempted both and would really appreciate it if someone could tell me if the answers look ok as I am really not sure whether i have correctly followed the method...

Homework Statement Part of a problems asks us to show that for a general function f(|r1-r2|)=f(R) that Div[f] only with respect to r1 is the same as Div[f] only with respect to R Homework Equations f(|r1-r2|)=f(R) The Attempt at a Solution I'm really unsure where to start, but I...

I am just curious how you find the divergence of the following vector field Heres my example u = xz^(2)i +y(x^(2)-1)j+zx^(2) y^(3)k Am I right in thinking U take the derivative with respect to x for first term derivative with respect to y for second term... giving me...