Terms Definition and 1000 Threads

as below, my math is getting rusty, hope some can help me out. thanks. \frac{1}{1+\frac{1}{x}}

Laurent series "throwing away" terms Homework Statement Veeeery similar to https://www.physicsforums.com/showthread.php?p=1868354#post1868354": Determine the Laurent series and residue for f(z) = \frac{1}{(e^{z} - 1)^{z}} Homework Equations We know that the Taylor series expansion...

Can anyone explain in laymans terms what a Kleins bottle is . I have encountered the definition that it is a non orientable surface , that it is a 2 dimensional manifold in 4 dimensions. I don't have a clue what a non orientable surface is , or what a manifold is . I also don't have any idea...

The Bernoullis Equation for an Incompressible Inviscid flow (say water) is as follows: p + (1/2).ρV^2 + ρgh = constant where, In words, static pressure + dynamic pressure + pressure energy due to height = constant It gives the Energy...

Does anybody have a reference or can write out the general (so not just a boost in only one direction) Lorentz matrix in terms of rapidities?

Homework Statement Find the first three terms of a geometric sequence given that the sum of the first four terms is 65/3 and the sum to infinity is 27. Homework Equations \begin{array}{1} S_n = \frac{a(1 - r^n)}{1 - r}\\ S_n = \frac{a(r^n - 1}{r - 1} \end{array} The Attempt...

I've been recently reading a book on abstract algebra and number theory, and I stumbled upon a problem that at first glance looked obvious, but I can't seem to figure out how to formally write the proof. 1.)So, let's say we have 4 integers, r,s,t,u, all greater than or equal to 1. Suppose...

Homework Statement I want to express sin(x) in terms of tan(x).Homework Equations tan(x)=sin(x)/cos(x) 1+tan2(x)=sec2(x)The Attempt at a Solution sin(x)=cos(x)tan(x) At this point I realize this is assuming x\neq \pi/2+k\pi cos^2(x)=\frac{1}{1+tan^2(x)} therefore...

Homework Statement Use the quadratic formula to solve the equation for (a) x in terms of y and (b) y in terms of x. Homework Equations 4x^2 - 4xy + 1 - y^2 = 0 The Attempt at a Solution I am not really sure where to start at all. If I could just figure out the values for a, b, and...

Homework Statement Find (in terms of the constant a) lim (√8(a+h) - √8a)/h h=>0 Homework Equations The Attempt at a Solution I tried a few ways of simplifying the numerator and trying to cancel out the h's but each time I try it doesn't come out right at all or I still...

Hello, I have some questions, but I'm not posting on quantum mechanics because as written in the FAQ, wave-particle duality is not really the realm of quantum mechanics, but is only a way for us to imagine what's going on. Is it true that the uncertainty on the location \Deltax, is in fact...

I"m starting to suspect that the existence of time is contingent upon the expansion of the universe. In other words, were the expansion to cease, time itself would come to a halt. As we know, as space accumulates thru expansion, time also accumulates. Thus, the space/time continuum is in fact...

Express Max height in terms of g and T?!? I need to express the y_max in terms of g and T... do i need to put in my V_0y value? or leave it as a variable? i've tried V_0y*T + 1/2gT^2

Homework Statement Show that the series \displaystyle\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n} is not absolutely convergent. Do so by permuting the terms of the series one can obtain different limits. Homework Equations The Attempt at a Solution I don't have a total solution...

The terms "function" and "map". I have noticed that the term "map" is used more often than "function" when a map/function is defined using the "mapsto" arrow, as in "the map x\mapsto x^2 ". It has occurred to me that when a function is defined this way, it's usually not clear what the codomain...

So I've been stuck on this problem for hours, I just can't seem to put the pieces together... Homework Statement Two basketball players of equal height, (and jumping with same initial velocity, etc.) by jumping they raise their centers of mass the same distance "H". The first player (A)...

Homework Statement L = \frac{a}{\sin{\theta}} + \frac{b}{\cos{\theta}} find L in terms of a and b where L is a maximum ... Homework Equations place long list of trigonometric identities here??The Attempt at a Solution so my attempt looks something like this: as a cause of the chain rule...

Any suggestions on how to simplify the log (m+1) terms that arise when proving the following statement using induction for m >= 1? (log to the base 2) [PLAIN]http://dl.dropbox.com/u/471735/recurrence%202.png

Could you please help me understand how these terms relate to one another? Scalar, Vector, Displacement, Distance, Speed, Velocity, Accelaration, Position? So Distance is a scalar Quantity, what is a Scaler? Displacement is a vector quantity, what is a Vector? Is velocity just the unit...

Homework Statement sum of first 11 terms of Ap is 17 and sum of first 17 terms is 11 find the sum of first 28 terms?Homework Equations Sum=n/2[2a+(n-1)d]The Attempt at a Solution i tried solving it by using obove formula but i am not able to do so as the value of d is coming in fraction

How could you describe qualitatively how diffraction of a wave through a aperture in terms of the uncertainty principle? Cat

Hello, do you have a hint on how to solve this limit? \lim_{x\to +\infty}(\sqrt{x^2+ax+b}-\sqrt{x^2-ax+b}) Thanks!

Hi, I'm am trying to calculate the radius of curvature of a trajectory in a plane. I am using Frenet-Serret formulas and perpendicular bisector approach to calculate the radius. It comes out that both the approaches lead to same answer when I calculate the radius for a trajectory generated...

Or provide any additional information or resources about them? I'm thinking about how light would react when passing through certain substance/or geometric medium 3 concepts come to mind when considering the idea 1 the light (beam, frequency notwithstanding) enters a prism and is...

Homework Statement The problem is in the attachment along with my answer. Can please one check if I got a correct answer? Some sources say the answer is 2Pi instead of just Pi. Homework Equations The Attempt at a Solution

So, the common high school physics example of a transverse wave is a "stadium wave" ... but, I'm wondering if this is actually longitudinal in terms of particle transmission. Each particle (audience member) is only standing up/down. The particles/audience stay in place and don't propagate/run...

Homework Statement Find x and y in terms of a and b from the following equations x * √x + y * √y = a x * √y + y * √x = b Homework Equations the general algebra equations The Attempt at a Solution adding the equations (x + y) * (√x + √y) = a + b x + y = a + b...

I'm reading a QFT text right now and to fully understand the physical perturbation theory method I would like anyone to suggest a refrence or supply an example of a calculation using the physical perturbation theory: As an example to start a discussion consider. L = \frac{1}{2}((\partial...

Hi, How can I write, for instance, the square root of (a2 + b2) in another form? Is there another expression which equals √(a2 + b2), and is it possible for that expression to have its √() holding one term whereas other factors exists outside the √() in that expression... Thanks...

edit: Oh nuts, embarrassing typo. Should be "...rearranged in terms of y" Ok, I swear this isn't homework but if it seems too much like homework I'm happy to have it moved there. So I need to be able to find x given y in: y = 1/(1+x)^x Possibly important: y will always be between 0 and 1 and...

um, I'm having a hard time understanding some terms and equations in semiconductors, particulary 2 equations and 1 term(fermi function,density of state function, and fermi level). My understanding of fermi function is somewhat the probability of an energy state to be occupied by an electron. for...

As it says in the title, will anyone please give me the equation (in pre-algebraic terms) for discrete choice probability? I can see that the equation is P = Prob( Person n chooses Alternative i ) = G(xni, xnj(forall j inequal to i), sn, β), where xni is a vector of attributes of...

I have been researching generators lately, whilst contemplating building my own wind powered generator. I think I understand the general layout: a central magnetic core that rotates with an outside ring of conductive coils spun in specific alternating turns with their own magnetic cores. If I am...

The terms "length contraction" and "time dilation" Is there a particular reason why we say length contraction but time dilation? A Lorentz transformation \Lambda=\gamma\begin{pmatrix}1 & -v\\ -v & 1\end{pmatrix} takes \begin{pmatrix}1\\ 0\end{pmatrix} to \gamma\begin{pmatrix}1\\...

sum up the series : 1/(1.3.5)+1/(3.5.7)+1/(5.7.9)+.......n terms.

Homework Statement Hi, I need to find the spectrum of the following function: i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]Homework Equations the Fourier Transform would be: \int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi...

http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png" How to rewrite this 2D Gaussian eqn in terms of x? i need to calculate the x and y values. let x0=0 and y0=0. is it complex?

I understand why dE=TdS-PdV ...[1] at constant temperature and pressure Also, I see that F=E-TS and therefore dF=dE-SdT-TdS ...[2] and how combining [2] and [3] gives dF=-SdT -PdV QUESTION: shouldn't [1] be expressed as dE=TdS+SdT-PdV i.e if you're going to substitute...

For instance: 1/(e^.5t) + 1/(e^-7t) As t grows larger, the left term goes to 0, but the right term goes to infinity. Would I be correct in saying that the limit of the sum is infinity because the (absolute value of the) coefficient of t in the term that tends to infinity is larger than...

Homework Statement Put in general terms 1, 1, -1, -1, 1, 1, -1, -1, ... Homework Equations The Attempt at a Solution obviously (-1)^n, alternates 1, -1, 1, -1... I have no idea how to figure this out. I thought it might have a sin function in it possibly. Thanks a lot for...

Homework Statement Find the explicit formula c1=1, c2=2, cn+1 = (cn + cn-1)/2 ; n>2 Homework Equations The Attempt at a Solution c1 = 1 c2 = 2 c3 = 3/2 c4 = 7/4 c5 = 13/8 c6 = 27/16 c7 = 53/32 c8 = 107/64 I know the bottom term is 2^n-2. I cannot find what the top...

Does anybody help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve. [\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex] where f(k,j) and [\tex]\theta_{k,j}[\tex] are some...

This is a question about solving Einstein's Field Equations for some simple cases, but I'm not sure how to explain this without analogy. So bear with me for a brief discussion. Consider the electrostatic equation: \nabla^2 V = \rho / \epsilon_0 which show explicitly how the charges source the...

The Von Neumann entropy is \mathcal{S}(|\psi\rangle) = -Tr[\rho_a ln \rho a] . The linear entropy S_L = \frac{l}{l-1}(1 - Tr[\rho_a^2]) For l =2 the linear entropy is written 4Det(\rho_A) which is also called the tangle \tau. I understand this just fine, I can show that. Now it says the Von...

Can anyone give some help on how I should go about creating a formula for this problem? Bob creates a new shade of paint by mixing black, red and white paint. He uses x litres of black paint. He uses 5 times as many litres of red paint than he uses of black paint. He uses 12 more litres of...

Homework Statement By first expressing the general term in partial fractions, find an expression in terms of n for summation of r=2 to n ( 1 / (r^2 - 1) ). Hence show that summation of r=1 to n ( 1 / r^2) i less than 7/4 for all values of n Homework Equations The Attempt at a...

Homework Statement Hi, I have this function: f(x ) = 0 (x is irrational) or f(x) = 1/q for rational p/q in lowest terms. show that this function is not differentiable anywhere The Attempt at a Solution This is the answer from the solutions book: consider [(f(a+h) - f(a ) ) /...

Hello everyone, Can someone please tell me what is the meaning of "lumped" term in heat transfer? Regards Huygen

Homework Statement Hi. Find the sum of the first 10 terms in the series: 1, (ln2)/1!, (ln2)^2/2!, (ln^3)/3!... Homework Equations I guess the Maclaurin series, which is e^k = 1, k/1!, (k^2)/2!, (k^3)/3!... In my case, k = ln2. The Attempt at a Solution I tried to use the sum of the first...

Homework Statement This is actually part of a probability problem I'm thinking about. I'm trying to find the nth moment of a certain random variable in terms of the gamma function, which is basically equivalent to solving the following integral or expressing it in terms of the gamma function...