Term Definition and 742 Threads

Hey! I have a question: how can you find the power-series solution and its leading term of the following ODE around the point x=+-(1-b) (where b is near x): $$-(1-x^2)\frac{\partial^2 f^m_l}{\partial x^2}+2x\frac{f^m_l}{\partial x}+\frac{m^2}{1-x^2}f^m_l=l(l+1)f^m_l ,$$ and m and l are...

Homework Statement ...For each of the temperatures...compute the second term in the virial equation ##B(T)/(V/n)##, for nitrogen at atmospheric pressure. Homework Equations ##PV = nRT(1+\frac{B(T)}{V/n}+\frac{C(T)}{(V/n)^2}+...)## The Attempt at a Solution I'm given a list of temperatures and...

Lets take QED just to simplify. When we are doing Path Integrals and we want to "fix the Gauge": 1 we add in the integral a delta(F) -meaning that we are going to integrate only in one representative of each class of equivalent configuration- 2 We take some factors out because they are constant...

Homework Statement Write down the general solution of the time-dependant schrodinger equation in terms of the solutions of the time-independant Schrodinger equation. Homework Equations TDSE TISE The Attempt at a Solution I'm really not sure how to interpret this question, I could write the...

Find the nth term of the sequence; ## 2, 5, 10, 17,26......## this is how i did it: 2, 5, 10, 17, 26 can form a difference of 3,5, 7,9... whose nth term is 1 + 2n. now how can apply this to the original sequence to get the nth term?

Homework Statement I have a PDE and I need to solve it in spherical domain: $$\frac{dF(r,t)}{dt}=\alpha \frac{1}{r^2} \frac{d}{dr} r^2 \frac{dF(r,t)}{dr} +g(r,t) $$ I have BC's: $$ \frac{dF}{dr} = 0, r =0$$ $$ \frac{dF}{dr} = 0, r =R$$ Homework Equations So, in spherical coord. First...

In the following program http://www.bbc.co.uk/programmes/b02144gl Penrose asserts that Einstein regretted the term relativity because it gave ammunition to those who assert that there is not one truth or that reality is a social construct. Does anyone have exact quotes from Einstein asserting...

Hey guys, This is really confusing me cos its allowing me to create factors of 2 from nowhere! Basically, the first term in the Lagrangian for a real Klein-Gordon theory is \frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi). Now let's say I wana differentiate this by applying the...

I'm a chemist trying to understand atomic term symbol. If we list all the micro-states of certain multi-electron configuration, these micro-states can be grouped into several certain terms characterized by L and S. In other words, when we compute the ML and MS for each of the micro-state, they...

No, I'm not asking what language to learn, etc. I started learning python last year and i was wrapping my head around the basic concepts and even making some nifty programs. However, one day I just got frustrated and gave up. I know frustration is common but I felt very stupid while...

I have heard different things and want to get a "professional" opinion on this. It seems like the words "term" and "expression" are technical terms with specific definitions in math and I want to know what they technically refer to (not just the personal slang or informal definitions someone...

I have been trying to find the nth term of the following sequence: -1, 5, -17, 65... I am thinking that the nth term has (-1) ^n . It doesn't appear to be a geometric or arithmetic sequence. I am stymied.

How does one set up the Runge Kutta for \frac {d^2y} {dt} m = b(\frac {dy} {dt} - \frac {dx} {dt}) + k (y-x) ? Set up the substitution variables: a = \frac {d^2y}{dt} v = \frac{dy} {dt} Then what ? Is there a way to get \frac{dx} {dt} out of the equation ? If not, I have to...

Homework Statement (\partial_t - A\nabla^2 + B)f(x) = \eta(x, t) So I have a homogeneous linear differential equation except for an added noise term ##\eta(t) ##. The noise is uncorrelated between times and has a Gaussian distribution with zero mean. That is we have Gaussian white noise...

Homework Statement Please see the attached file. Homework EquationsThe Attempt at a Solution If my math is right so far, I am basically stuck as to what to do with the E(t) term. [/B]

I know this is physics forums and I am a physicist. I figure the people out here are well read beyond the realm of physics. I am trying to remember the term that describes a country should expand its borders based on religious belief. I am writing a paper, and I cannot come up with the name of...

When a singer is performing a song, and they're singing syllables which are not words or have any meaning, but only have some aesthetic quality. For example, "la la la" or here in this song from about 2:25-2:50 What is the term or word for this?

Hey again! (Smile) I want to find the complexity of $g(n)=10 \cdot \log (n^{30}+30)+2 $. We will find that $g(n)=\Theta(\log n)$, right? (Thinking) What can I say at the beginning? Which is the dominant term of the function? (Thinking)

Homework Statement I need to (analytically) solve a system of coupled second-order ODEs: (A) \frac{du}{dt} - fv = \Omega^2x (B) \frac{dv}{dt} + fu = \Omega^2y where u = \frac{dx}{dt} v = \frac{dy}{dt} subject to the initial conditions u(t=0) = U and v(t=0) = 0. Homework Equations --- The...

Hello, What is the meaning of term "Framework" (Programming Environment). I've usually keep hearing this term, But didn't understand the meaning. Suppose we we say .NET Framework, then what actually does it refers.

Homework Statement The simple regression model is y = α + βx + u, where u is the error term. If you don't include α, when is β unbiased? Homework Equations y = α + βx + u The Attempt at a Solution Not including α doesn't affect whether β is unbiased because α is a constant.

Homework Statement Find the general term and test the nature of the series: Homework Equations 1+1*4+1*4*7+... The Attempt at a Solution Term N = Term (N-1) * 3N-2 Hence,3(N-1)-2 * 3N-2 which simplifies to (3N-5)(3N-1) = 9N^2 - 18N + 5 Is this correct?

Homework Statement Find the general term and test the nature(convergent/divergent) of: 1/3 + 2/15 + 2/35 + ... The Attempt at a Solution If I simplify I get , 1/3 + (1)(2)/(3)(5) + (1)(2)(3)/(3)(5)(7) +.... I found that, TERM(N) = TERM(N-1)((N)/(2N+1) After this I am struck.

Homework Statement IF e^{m \arctan x}=a_0 + a_1x + a_2x^2 + a_3x^3...+a_nx^n+... prove that (n+1)a_{n+1} + (n-1)a_{n-1}=ma_n and hence obtain the expansion of e^{m \arctan x} . Homework Equations The Attempt at a Solution $$e^{m \arctan x} = 1+m \arctan x + (m \arctan x)^2/2! + (m...

Homework Statement how do we get the n th term of a sequence if it is given in form of ##x_{ n+1 }=f({ x }_{ n })## and the p th term is given Homework Equations I figured we may get it if we get it in the form of ##x_{ n+1 }-{ x }_{ n }## but how?can we even get it?if yes,under...

Homework Statement Find the general term of 0, 4, 22, 118, 718, 5038, 40318 if a1 = 0, a2 = 4 and so on. The Attempt at a Solution I have tried getting the differences between them, even going 4 levels deep, but that isn't working obviously, I tried seeing if the ratios are the...

Homework Statement Solve \frac{\partial v}{\partial t} = k\frac{\partial^2 v}{\partial x^2} - v 0\leq x \leq L t > 0 Homework Equations v(x,0) = f(x), v(0,t)=0, \frac{\partial v}{\partial x}(L,t) = -v(L,t) The Attempt at a Solution I've already attempted to solve...

I am trying to derive part of the navier-stokes equations. Consider the following link: http://www.gps.caltech.edu/~cdp/Desktop/Navier-Stokes%20Eqn.pdf Equation 1, without the lambda term, is given in vector form in Equation 3 as \eta\nabla^2\mathbf{u}. However, when I try to get this from...

I wanted to factor xy+x-2y-2 I got x(y+1)-2(y-1) and got stuck I tried somethings out and noticed (x-2)(y+1)=xy+x-2y-2 so how come I did get stuck? Did I extract the 2 incorrectly with the sign? For example should I have interpreted it at -2y-2 not 2y-2?

I'm trying to do some refreshing of differential equations featuring damped systems. Specifically, I have a question regarding the differential equation solution to an under damped system involving complex roots. Referring to the attached pdf, an under damped system will yield a complex...

Hi All, This is from a classical mechanics problem, and I already 'solved' the problem, but I'm interested in why a certain term is set to zero. I think I understand the concept but just want to clarify. The problem is a table with a hole in it and two masses on a string, one mass is...

I am studying the behavior of the magnetic fields between the rotor field and stator field(armature reaction) in a synchronous generator . I understand that the stator magnetic flux will vary depending on the power factor of the load (leading, lagging or resistive). If the load is resistive, the...

Homework Statement Find the formula for nth term of: ... , -450 , -270 , -180 , -90 , 90 , 180 , 270 , 450 , ... Homework Equations Arithmetic and geometric series Recursive The Attempt at a Solution Usually when finding the formula of Un, n starts from 1. But since the pattern...

Homework Statement The givenequation is this: \frac{1}{4} \frac {du}{(2-u)} \ + \ \frac{1}{4} \frac{du}{(2+u)} \ = \frac{dx}{x} My book says that when integrated, the above equation becomes \frac{-1}{4} \ln (2-u) \ + \ \frac{1}{4} \ln (2+u) \ = \ln (x) + \frac{1}{4} \ln (c) I...

For certain types of functions I have been using the term 'general form' as a way of stating that some function of some variable(s) is true for more than one value of the variable (usually an infinite number). Here is a simple example, 1=cos(2∏x) There have been (at times) where the use of...

I'm looking for proof that Wolfgang Rindler coined the term Event Horizon. I believe that it was Rindler because that's what I've heard from reliable sources, e.g. http://www.mathpages.com/home/kmath339/kmath339.htm Thank you in advance.

I read some of the articles related to particle physics experiment and don't know the meaning of it. 1. minimum bias event 2. pile up Also, η (pseudo-rapidity) is used instead of θ to describes the angular distribution, but why ? Can someone explains to me ?

For twice differentiable path x:[t_A,t_B]\to\mathbb{R}^N the action is defined as S(x) = \int\limits_{t_A}^{t_B} L\big(t,x(t),\dot{x}(t)\big) dt For a small real parameter \delta and some path \eta:[t_A,t_B]\to\mathbb{R}^N such that \eta(t_A)=0 and \eta(t_B)=0 the action for...

why the topological term in gauge theory, ε_{\mu\nu ρσ}F^{\mu \nu} F^{ρσ} ,is scale-independent?

In case you have the Kahler and super- potential K,W: K(T,S,C) = -log (S +S^{*}) -3 log ( T+ T^{*} - C C^{*}) W(T,S,C)= C^{3} + d e^{-aS} +b with T,S,C chiral super fields, b,d complex numbers and a>0. I tried to calculate the local F-terms arising from this. The local F-terms for the i-th...

How do you write out the potential of an ion in a Penning trap? Specifically, how does the inter-ionic Coulomb interaction come to be written as a Green's function? I found it here : http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.71.87 They do say something about interactions with image...

1. Write down the general term of each of the following sequences in simplest form: So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ... I really need to find an equation that I...

It's part c I don't understand, why the expectation value equals to solid angle * sin3 i? I mean, what role does the solid angle play? Thank you

I've got a term paper due in a couple of weeks and I need to find a historical physicist to write it about. The paper will highlight his/her's contributions to physics and will be a bit on the technical side (including equations, maybe some derivations and proofs). I was wondering if anyone had...

I have a problem understanding the attached part of the book... Specifically how they derived this result for the Fs... For example I'll try to write: F_{1}^{\dagger}= - \frac{\partial W(Φ_{1},Φ_{2},Φ_{3})}{\partial Φ_{1}}|_{Φ_{1}=φ_{1}} If I do that for the O'Raifeartaigh superpotential I'll...

I am currently a freshman in a top 20 school. I am midway through my last term of the first year. I am depressed, far away from home, and my grades are falling(since the last term's finals). I am considering withdrawing for the term just to regain my peace of mind and life. I will probably be...

Homework Statement i got stucked here. below is the answer given. can anybody help please? Homework Equations The Attempt at a Solution

Is the term "loop" loosely defined in Faraday's law? A voltage will be induced in a loop of wire when the magnetic field flux through the loop changes If you're reading this, you probably know what happens when you hook up the leads from an oscilloscope to a microphone. Nothing, lol. There...

My mind has gone blank and I've suddenly forgotten basic algebra, please could someone give me direction on how to make P the subject of this equation? E = (P^2 C^2 + M^2 C^4)^1/2 + (P^2 C^2)^1/2 thanks for any help

Homework Statement {a_n} and {b_n} are two sequences given by a_n = (x)^{1/2^n}+(y)^{1/2^n} and b_n = (x)^{1/2^n}-(y)^{1/2^n}. Then find a_1 a_2 a_3 ... a_n in terms of x,y and b_n Homework Equations The Attempt at a Solution I tried substituting n=1,2,3 and so on for a few...