Terms Definition and 1000 Threads

Does anyone have a link to a version of the EFE fully expanded in terms of the metric?

I'm a bit confused with limits of big-O terms. What should be the answer for following:- 1) limit of O(1/x) as x->0. O(1) maybe but I'm not sure. 2) limit of O(x) as x-> 0. O(1) or 0?

Homework Statement Let k be a constant. If α and β are the roots of the equation 3x^2 + 2x - k = 0, find the value of 3α^2 - 2β in terms of k. Homework Equations The Attempt at a Solution Obviously, the usual αβ = -k/3 α + β = -2/3 has been written but I couldn't put them...

if ψ(o)=(1 0)^{T} at time t=0. According to some Hamiltonian, it was found that the corresponding eigenstates are |ø_{1}> = 1/√2(1 i)^{T} and |ø_{2}> = 1/√2(1 -i)^{T} so then we wanted to expand ψ(0) in terms of |ø_{1}> and |ø_{2}>: the author got: 1/√2|ø_{1}> + 1/√2 |ø_{2}> My question is...

I am trying to write the Einstein field equations $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu} R=\frac{8\pi G}{c^4}T_{\mu\nu}$$ in such a way that the Ricci curvature tensor $$R_{\mu\nu}$$ and scalar curvature $$R$$ are replaced with an explicit expression involving the metric tensor $$g_{\mu\nu}$$...

Homework Statement Hey. I need help simplifying and factoring a differential equation in terms of v and p (velocity(xdot) and position(x) respectively). I need the final answer to be in this form: a = ( )v + ( )p. This is so i can put the governing equation in a state-space and eventually use...

All analitic function can be express how: f(x) = \frac{1}{0!} \frac{d^0f}{dx^0}(x_0) (x - x_0)^0 + \frac{1}{1!} \frac{d^1 f}{dx^1}(x_0) (x - x_0)^1 + \frac{1}{2!} \frac{d^2f}{dx^2}(x_0) (x - x_0)^2 + \frac{1}{3!} \frac{d^3f}{dx^3}(x_0) (x - x_0)^3 + ... that is the taylor series of the function...

Homework Statement This isn't exactly a homework question, but I figured this would be the best subforum for this sort of thing. For the sake of a concrete example, let's just say my question is: Express the position operator's eigenstates in terms of the number operator's eigenstates...

Homework Statement A general rotation through angle ##a## about the axis ##\underline{n}##, where ##\underline{n}^2 = 1## is given by $$R(a,\underline{n}) = \exp(-ia\underline{n} \cdot \underline{T}),$$ where ##(T_k)_{ij} = -i\epsilon_{ijk}##. By expanding the exponential as a power series in...

Homework Statement ∫(a= -3 , b= 0) (1 + √9 - x^2) dx Homework Equations ∫(a,b) f(x) dx = lim as n → \infty \sum f(xi) delta x The Attempt at a Solution I tried plugging in my a and b value into the function just as I would with any other function to find the area and i get a number...

Hello! Well, I guess it's all in the title, really. I was reading about k-essence, and it was described as a scalar field having a non-canonical kinetic term. I did a bit of browsing and couldn't find a clear explanation of what, exactly, a non-canonical kinetic term is. Any help would be...

We can represent π, in terms of primes by using Euler's product form of Riemann Zeta. For example ζ(2)=(π^2)/6= ∏ p^2/(p^2-1). Likewise, is there a representation of e that is obtained by using only prime numbers?

find parametetric representation of 3 perfect squares which are successive terms in AP ($x^2$,$y^2$,$z^2$) such that $x^2,y^2,z^2$ are successive terms of AP. find x,y,z

This is how one poster tried to explain it to me but for people who have only taken a basic physics course in college it leaves a lot wanting. "If a system is in a pure state, and you know what the pure state is, then your knowledge of the system is complete, and all uncertainty is quantum...

A limit of a sequence is definitely convergent if: If for any value of K there is an N sufficiently large that an > K for n > N, OR for any value of K there is an N sufficiently large that an<±K for n > N My only question is what exactly are K, N, an and n? What values are they? How would...

How do you find the inverse of metric tensor when there are off-diagonals? More specifivally, given the (Kerr) metric, $$ d \tau^2 = g_{tt} dt^2 + 2g_{t \phi} dt d\phi +g_{rr} dr^2 + g_{\theta \theta} d \theta^2 + g_{\phi \phi} d \phi^2 + $$ we have the metric tensor; $$ g_{\mu \nu} =...

I wonder what parts of statistics have specific terms existing for them - I see a relevant notion which would be relevant, but not sure if there is a term for it. If variable values can be ordered then it possesses a median. If the values can also be added then they also possesses an average. A...

Homework Statement "In a geometric sequence, the sum of t7 and t8 is 5832, the sum of t2 and t3 is 24. Find the common ratio and first term." Homework Equations d = t8/t7 or t3/t2 tn = a * rn-1 The Attempt at a Solution So I thought of developing a system of equations then solving...

Prove that $\tan \left( \dfrac{3 \pi}{11} \right)+ 4\sin \left( \dfrac{2 \pi}{11} \right)=\sqrt{11}$. I know this problem may be stale as it has been posted countless times at other math forums, but I've seen one brilliant method to attack this problem recently, and I'm so eager to share it...

I was trying to design some GUI for a tool I'm making and I noticed there's a hidden math problem somewhere in there. Not being one to let the opportunity slide, I decided it's worth exploring. Basically there's 3 buttons that add to a variable. What are the best values to put on those...

Hellow! I was noting that several definitions are, in actually, expressions of vector calculus, for example: Jacobian: \frac{d\vec{f}}{d\vec{r}}=\begin{bmatrix} \frac{df_1}{dx} & \frac{df_1}{dy} \\ \frac{df_2}{dx} & \frac{df_2}{dy} \\ \end{bmatrix} Hessian: \frac{d^2f}{d\vec{r}^2} =...

There are multipliers that can be used when building infinite series that can create several different orders for the signs of consecutive terms by, for example, (-1)^n to get, - + - + - +... but I have been having difficulty figuring out any beyond the following, + - + - + -... + + -...

Homework Statement Sum the series 1 + 2a + 3a2 + ... to n terms This series consists of an a.p. (with general term n) and gp general term a^(n-1) right? So the series general term is na^(n-1) So is the sum the sum of each progression times each other? i.e (1-a^n)/(1-a) *...

Hi, All: Sorry for the length of the post, but I think it is necessary to set things up so that the post is understandable: I'm going through an argument in which we intend to show that a given vector field [ itex]R_ω [/ itex] (actually a Reeb field associated with a contact form ω) is...

Evaluate the sum $\displaystyle \sum_{i=0}^n \tan^{-1} \dfrac{1}{i^2+i+1}$.

In a previous thread I showed how to express $\zeta'(-1)$ in terms of the Glaisher-Kinkelin constant. http://mathhelpboards.com/challenge-questions-puzzles-28/euler-maclaurin-summation-formula-riemann-zeta-function-7702.html This thread is about expressing $\zeta(3)$ (sometimes referred to as...

Homework Statement . Let ##f:[a,b] \to [\alpha,\beta]## be a bijective function of class ##C^2## with an inverse function also of class ##C^2## ##g:[\alpha,\beta] \to [a,b]##. a)Calculate ##g''(x)## for every ##x \in (\alpha,\beta)## in terms of ##f## and its derivatives. b)If ##f'(x)>0##...

As I understand it, the value of a 4-vector x in another reference frame (x') with the same orientation can be derived using the Lorentz boost matrix \bf{\lambda} by x'=\lambda x. More explicitly, $$\begin{bmatrix} x'_0\\ x'_1\\ x'_2\\ x'_3\\ \end{bmatrix} = \begin{bmatrix}...

Hello (Smirk) Given the x^{2}y''+axy'+by=0,I have to show that with replacing x with e^{z},it becomes a second order differential equation,with constant terms. I tried to do this and I got this: y''+\frac{a}{e^{z}}y'+\frac{b}{e^{2z}}y=0 . But,at this equation the terms aren't constant...

Homework Statement Given the following wave function for hydrogen: psi(r, t=0) = (1/sqrt(10))*(2*psi_100 - psi_210 + sqrt(2)*psi_211 + sqrt(3)*psi_21(-1)) where the subscripts show n, l, m_z, respectively, and the psi_nlm_z are already normalized. - At t=0, we measure and find l = 1...

Hi All, I'm working through the theory of the strong interaction and I roughly follow it. However I have some questions about the meaning of the terms. The book I use gives the gauge transformation as: \psi \rightarrow e^{i \lambda . a(x)} \psi First question ... What are the a(x)...

In my text it's given when a cube underwents a uniform unit tensile force be applied in all six faces, bulk module=1/3(α-2β) Where α is longitudinal strain and β is lateral strain.is there a derviation for it..? And it states in x direction there will be increase in length and in y, z...

Let f(x+iy) = \frac{x-1-iy}{(x-1)^2+y^2} first of all it asks me to show that f satisfies the Cauchy-Riemann equation which I am able to do by seperating into real and imaginary u + iv : u(x,y),v(x,y) and then partially differentiating wrt x and y and just show that \frac{\partial...

What is Schwinger terms that related with commutator of currents and what is the origin?Why the infinities appear when we consider the product of operators of fields at the same spacetime point?

How does one calculate the number of terms in the sequence \sum\limits_{a=2}^k \sum\limits_{b=a}^k of 1/(a*b).

Hi guys, i need your help to go about his question, Question: $$\text{Show that the coefficient }C_n \text{in the Laurent expansion of }$$ $$f(z)=(z+\frac{1}{z}) \text{ about z=0 is given by}$$ $$C_n=\frac{1}{2\pi}\int^{2\pi}_0 \cos(2cos(\theta))cos(n\theta)\, d\theta ,n\in\mathbb{z}$$

Homework Statement Find an expression for the moment of inertia (I) of the platform in terms of acceleration of the mass (a), the value of the hanging mass (m), the radius of the spindle (r) and the constant (g). Diagram: http://i.imgur.com/rv3zFYG.jpg Homework Equations F=ma t=Iα...

What Is The Difference Between These "Dielectric" Terms? Can someone please explain to me what the difference between these terms are? 1. Dielectric constant 2. Relative dielectric constant 3. Dielectric loss I came across them on this website: http://www.lsbu.ac.uk/water/microwave.html#pen...

This is a spin off from another thread: First there are a couple of mathpages http://mathpages.com/rr/s8-04/8-04.htm and http://mathpages.com/rr/s8-03/8-03.htm that discuss the refractive index model and highlights the differences. The first obvious objection is that the 'medium' must have...

Hi, I need to let an operator act on a scalar function. The operator is however in a very cryptic form, so I would want to work it out a little bit. I get stuck in the process. The operator is: \vec{u}\cdot\left[\vec{L}\times\left(\vec{u}_r\times\vec{L}\right)\right]f Where \vec{L} is...

If you have the equation \frac{dx}{dt}=4(x^2+1) I sometimes get confused if i should should subtract 4(x^2+1) from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but...

how would i go about properly grouping terms to start my factoring? 1. $12x^2y^3-24y^3z-6x^6+30y^4-15x^4y+4x^2y+12x^4z+10y^2-8yz$ thanks!

I want sthg I can visualize in order to understand , I keep asking and am always told time , so how is time a 4th dimension ? I try my best but my mind is too weak to visualize things more complex than disney (so please , I want sthg in that standard ,consider me a curious 6 year old child)

Hi MHB, This problem vexes me until my mind hurts. Problem: Find the sum of the first 11 terms of the series \frac{19}{99}+\frac{199}{999}+\frac{1999}{9999}+ \cdots Attempt: I managed only to find the expression of the nth term of the given series and I got...

Homework Statement If \displaystyle \int_0^1 \dfrac{e^t}{t+1} dt = a then \displaystyle \int_{b-1}^b \dfrac{e^{-t}}{t-b-1} dt is equal to Homework Equations The Attempt at a Solution I used the definite integral property in the second integral \displaystyle \int_{b-1}^b...

1. Background/theory We know that if the equation x3+px2+qx+r=0 has solutions x1, x2, x3 then x1 + x2 + x3 = -p x1x2 + x2x3 + x3x1 = q x1x2x3 = -r 2. Problem statement Find (x1 - x2)2(x2 - x3)2(x3 - x1)2 as an expression containing p,q,r. That is, I'm supposed to find the discriminant of...

Homework Statement 3x+cos 2x = c c is an unknown constant. how do i solve x in terms of c?

This was something I noticed as I was trying to practice solving PDEs using the method of characteristics. The text has the following example: $$\frac{\partial u}{\partial x} + x \frac{\partial u}{\partial y} = 0$$ This should be easy enough. I let p(x,y) = x and solve for \frac{\partial...

I posted this question over at the QM page, https://www.physicsforums.com/showthread.php?t=714076 but I realized I am really looking for a hard Mathematical proof ... A description of a numerical way of proving this would also be very helpful for me. or a reference covering the...

Hi, Wasn't sure if I should post this to Linear Algebra or here. My question is really simple: Can a 2N by 2N random, and Hermitian Matrix ( Hamiltonian ) be always written as: H = A \otimes I_{2\times 2} + B \otimes \sigma_x + C \otimes \sigma_y + D \otimes \sigma_z where A,B,C,D are all...