Divergence Definition and 746 Threads

What is wrong with this logic? Homo Sapien 1. 46 (diploid) chromosomes 2. 32,185 genes 3. 3,079,843,747 bases (DNA bases A,C,T,G) 4. Homo sapines diverged from chimpanzees 6 million years ago. 5. There is a 3% difference in the genetic makeup of a homo sapien and a chimpanzee. 6...

Homework Statement For x_{n} given by the following formula, establish either the convergence or divergence of the sequence X = (x_{n}) x_{n} := (-1)^{n}n/(n+1)Homework Equations The Attempt at a Solution This is for my real analysis class. I tried to use the squeeze theorem, but didn't get...

\displaystyle\sum_{n = 1}^{\infty}\frac{(n!)^3}{(3n)!}z^n , \ z\in\mathbb{C} By the ratio test, \displaystyle L = \lim_{n\to\infty}\left|\frac{[(n + 1)!]^3 z^{n + 1} (3n)!}{[3(n + 1)]! (n!)^3 z^n}\right| = \lim_{n\to\infty}\left|\frac{z (n + 1)^2}{3}\right| = \infty. Therefore, the series...

Please teach me this: Why we do not consider the divergences in loops in QED when p^{2}→m^{2} but only consider the soft photon when k^{2}→0(IR divergence) and UV divergence? Thank you very much in advance.

Homework Statement http://s1.ipicture.ru/uploads/20120120/eAO1JUYk.jpg The attempt at a solution \int\int \vec{F}.\hat{n}\,ds=\int\int\int div\vec{F}\,dV where dV is the element of volume. div\vec{F}=3 Now, i need to find dV which (i assume) is the hardest part of this problem. I've drawn the...

Homework Statement What's the difference between Green's theorem, Gauss divergence theorem and Stoke's theorem? The attempt at a solution I'm struggling to understand when i should apply each of those theorems. Here is what i understand. Please correct my statements below, if needed. Green's...

I'm trying to understand why the del operator is working a certain way. So in my literature there is a term: \nabla \cdot \rho_a \mathbf{v} but then after saying that \rho_a=w_a\rho the term can somehow become \rho (\mathbf{v}\cdot \nabla w_a) I do not understand how nabla and the...

Homework Statement Given a vector field \textbf{F} and a composite (with this I mean cuboids, cylinders, etc. and not spheres for example) surface S, how do I calculate the flux through only some of the sides of S? I am interested in a general way to do this, but right now I am struggling with...

Infrared contribution of vertex correction gives an infinity, the resolution is to add infrared bremsstrahlung contributions as well, I can follow the math, but I'm not so convinced by the justification of this resolution given by Peskin(and Weinberg, and whatever I can find on internet)...

Hello, I am having trouble confirming that the flux integral is equal to the divergence over a volume. I am making a silly mistake & its just one of those days that I can't eyeball it. Here is the problem. I want to compute the flux integral for \vec{ F}=x\hat i+y\hat j-z\hat k...

Homework Statement Use a valid convergence test to see if the sum converges. Ʃ(n^(2))/(n^(2)+1) Homework Equations Well, according to p-series, I'd assume this sum diverges, but I don't know which test to use. The Attempt at a Solution I probably can't do this, but I was think...

del^2(\Phi^2)=( 2\Phidel^2)(2||grad\Phi||^2) typing out my entire solution will take me ages so I'm going to verbally explain what I've done. I tried to work on the right side of the equation to compress it and make it equal to the left side. it just isn't working. I took the magnitude of the...

Is the sum of 2 divergent series Ʃ(an±bn) divergent? From what I have learned is that it is not always divergent. Is this true? I believe that is what the picture i included is saying, but i maybe miss interpreting it. Also, is the product of 2 divergent series divergent or convergent?

Hi, I'd like to know the solutions for these equations, and how to arrive at them. Is it possible to derive the general form of F(x,y,z) analytically? I'm still studying linear differential equations so I have no clue on what to do with partial differential equations... div F = 0 curl F = 0...

Homework Statement Use the Divergence Theorem to evaluate ∫∫S (8x + 10y + z2)dS where S is the sphere x2 + y2 + z2 = 1. Homework Equations ∫∫S F dS = ∫∫∫B Div(F) dV The Attempt at a Solution I dunno, this isn't a vector field so I don't know how to take the divergence of it so...

Prove that every divergence free vector field on R^n, n>1 is of the form: v(x)=SUM dAij/dxi *ej where Aij(x) is smooth function from R^n to R such that Aij(x)=-Aji(x) i.e. matrix $[Aij(x)]$ is skew symmetric for every vector x.

Homework Statement So this is part of a problem set in which I have to show that a vector field is divergence free but not the curl of any vector field. LetF =\frac{<x,y,z>}{(x^2 + y^2 + z^2)^{3/2}} Then F is smooth at every point of R3 except the origin, where it is not defined. (This...

Homework Statement http://img593.imageshack.us/img593/5713/skjermbilde20111204kl11.png The Attempt at a Solution I thought it seemed appropriate to use divergence theorem here: I have, div F = 0 + 1 + x = 1+x I let that 0≤z≤c. If, x/a + y/b = 1then y=b(1-x/a) x/a +z/c = 1 then...

I am trying to verify the divergence theorem by using the triple integral and the surface integral of the vector field dotted with dS. No trouble per se, I'm not sure though about one thing: I am given a function and six planes (they form a cube). When I set x=0 the vector field is given as...

Ʃ ,n=1,∞, (2/n^2+n) Does this series converge or diverge? Im not sure how to start can i use the comparison test here?

Homework Statement Determine if the following series converges or diverges. If it converges determine its sum. Ʃ1/(i2-1) where the upper limit is n and the index i=2 Homework Equations The General Formula for the partial sum was given: Sn=Ʃ1/(i2-1)=3/4-1/(2n)-1/(2(n+1) The...

Homework Statement Let r = x i + y j + z k and R = |r|. Let F = r/R^p. find div(F) in terms of r.. i can't figure out how to express it in therms of r Homework Equations div(F) = the gradient added together

I suppose this has to go under homework, so here it goes: I'm in Calc III and we won't have enough time to cover the last chapter in the textbook about Stokes theorem, Green's theorem, and the divergence theorem, so instead the teacher wants a 7-page paper on something from that chapter. She...

Homework Statement i have the divergence in the (x,y,z) Cartesian as \frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz} and the assignment is to transfer it to cylindrical system (r,{\phi},z), by any way i choose. Homework Equations tried with the chain rule, but i am doing...

HI experts i want to know the physical significance of divergence theorem i.e how volume integral changes to surface integral - how can i explain in simple words.

Homework Statement I need to understand and prove the following: That if a>1 the function diverges, except for a special case x_0= b/(1-a). Then if a=-1 diverges for some cases and converges if x_0 is b/2. Again, not to clear on this. Homework Equations lim n →∞...

How do you prove that Maxwell's energy-momentum equation is divergence-free? I don't know whether or not I have to use Lagrangians or Eistein's tensor, or if there's a simlpler way of expanding out the tensor.. ∂_{\mu}T^{\mu\nu}=0...

How do you prove that the energy-momentum tensor is divergence-free? ∂μTμν=0

Hey there.. Basically I'm struggling with convergence and divergence of series. I can see if converges and diverges by common sense and thinking through in my head but I struggle to write it down. The definitions in books seem confusing. Are there any steps I can systematically do every...

Homework Statement \sum_{n=2}^{\infty} \frac{(-1)^n}{\sqrt{n} + (-1)^n}Homework Equations This is in the section covering alternating sequences. Leibniz's rule, conditional/absolute convergence, Dirichlet's test, and Abel's tests were all covered.The Attempt at a Solution I don't know what to...

I am trying to summarise the concept of divergence. Say I have a vector field, that is radially spreading outwards from the (0,0), but all vectors are equal in each point. So there are no deviations in magnitude in vectors(is that even possible?), but the field lines are spreading like in...

Is it? If so, can you show how? Thanks :smile:

Quick question… what does the following simplify to? Can it be written in any other way? \nabla\bullet (a \bullet b)b where a and b are vectors. Thanks,

How do you interpret the divergence or curl of the unit normal defined on a surface? This sometimes comes up when applying Stokes' theorem. A simple example would be Surface area = \int_{S} \hat{n} \cdot \hat{n} dA = \int_{V} \nabla \cdot \hat{n} dV where S is the closed surface that...

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.