Terms Definition and 1000 Threads

I might as well get a reaction on these idle thoughts or I will continue to think them. Something must be left over from schoolroom or uni because it seems to me a number mathematical terms have been incorporated into everyday or colloquial language. One that I think is relatively recent is...

is there a way to factor terms in non polynomials for example, to factor out (e^t)*t^2, (e^t)*t e^t t^2 (b + a t) + e^t (2 b + 6 a t) + e^t (2 b t + 3 a t^2) - 2 (e^t (2 b t + 3 a t^2) + e^t (b t^2 + a t^3)) + e^t (2 b t + 3 a t^2) Log[e] + e^t (b t^2 + a t^3) Log[e]

Top of page 69. I get six second order terms. Two of them cancel. Two are the ones on the right of 3.11. The other two involve KμKμ and KνKν. Why are there no such terms on the right of 3.11? I'm probably just missing something painfully obvious.

Greeting Physics Forums, I run a tiny online magazine and am trying to explain to my readers the difference between ceramic and magnetic cartridges. In particular, I'm trying to explain the how each type equalizes the audio signal in accordance to the http://en.wikipedia.org/wiki/RIAA_curve"...

Homework Statement Find the first four non-vanishing terms of the Taylor series for xcotx in the neighborhood of x = 0. Homework Equations The Attempt at a Solution LaTex isn't working for me so hopefully this doesn't look too messy. cotx = cosx/sinx. I know what the...

Homework Statement To find the general series expansion (1-x)^-1 for the first 4 terms Do i just use the taylor series ? Homework Equations f(x) = f(x) + f '(x)/1! x + f ''(x)/2! x^2 + f '''(x)/3! x^3 The Attempt at a Solution = 1 + x + x^2 + x^3 + x^4 etc. regards Brendan

hey, I'm having a good deal of difficulty understanding why the following expansion has an infinite number of terms within it: (1+x)n (|x|<1 where n is any real number) Would someone mind explaining this to me please? Thanks, Oscar

I'm trying to ge my head around some basic things but where ever I look I seem to get a different answer. what is an eigenvalue, eigenvector, eigenfunction and eigen stat, all in the context of QM? and how do these apply to the operator equation. \hat{O} \psi = O \psi what is the...

Homework Statement find the integral from 0 to infinity of t^(-1)*e^(-st) dt Homework Equations e^x series expansion The Attempt at a Solution I expanded e^(-st) into its series and then integrated, it appears to diverge since when the limits are plugged in terms become infinite...

I know that the effective action can be written as a double expansion in derivatives and loop (h-bar). For example, take the effective action for a real scalar field: \Gamma[\phi]=\int...

Hi! I'm writing a pool simulation program and have an awful problem with my ball collisions (elastic collisions). The theory (in terms of vectors) is that when two balls collide you take the line between their centers and the velocity components which are perpendicular to this line are...

Homework Statement Hot-air balloon of mass M is descending straight down with acceleration a. How much Mass must be discarded to make acceleration a the same magnitude, but directly up instead of directly down? Disregard wind resistance/lift. Homework Equations The only one my book...

I thought we can always cancel terms out and that its absolutely acceptable but then it turned out that I can`t cancel out the term "x-2" from "(x^2 - 4)/(x-2)" is this exception only for functions? and I have a 2nd question, and I know I should read on logic first, but PLEASE! I want to...

I'm taking 5 mins (hours) during some down-time to remind myself of some theory. Taking a simple Abelian Higgs model, where the Lagrangian is given by: \mathcal{L} = |D_\mu\Phi|^2 - \frac{1}{4}F_{\mu\nu}F^{\mu\nu} - V(\Phi) With the covariant derivative, field strength tensor and potential...

My teacher wrote an alternative equation on the board for curvature, and I am wondering how it is true: k = | dT/dt / |dR/dt| | where T is the unit tangent vector. I know k = |R' x R''| / |R'|^3 = |dT/ds| but I am not sure about the formula in question. How is it true/derived?

Hi I was wondering if there is a non-numericla way to solve the following equation: 144 - 90sin x - 155.8cos x = 0 Thanks

I'm upset, I just had my first physics test and I got a B+/A-, depending on how the professor gives partial credit. This is horrible news, the material was really simple and I'm sure most of you would think the test was trivial even for physics I. I don't get why I can do so good in pure...

Homework Statement a. The first part of this problem was to derive the escape speed (Vesc) for a star of mass M and radius R. b. The second part is where I am having trouble. It says to equate the Vesc calculated above and derive a formula for Planck length in terms of c, G, and h_bar...

Homework Statement A box of mass (m) is held against a frictionless wall by a force of magnitude F at an angle \theta (above right). Determine F in terms of whatever variables are necessary. Similarly, determine the magnitude of the normal force (n) in terms of whatever variables are...

In lecture in my real analysis course the other day we were proving that absolute convergence of a series implies convergence. Our professor started off by showing us the wrong way to prove it: \left| \sum_{k=1}^\infty a_k \right| \leq \sum_{k=1}^\infty \left| a_k \right| < \epsilon Then he...

Homework Statement I am asked to find a "compact expression" for the infinite sum: S(x) = 1 + e^(ix) + e^(2ix) + e^(3ix) +...+ e^(i*n*x) I am given a hint: "Note that it isn't true that S(x)-1= S(x)*e^(ix), but almost. Use this fact." Homework Equations e^(ix)=cos(x) +...

I'm having a bit of trouble getting the right answer for a problem in my electrical engineering textbook. The question is: At t=0, the current flowing in a 0.6H inductance is 8A. What constant voltage must be applied to reduce the current to 0A at t=0.4s. I'm using the equation...

Hi there! My physics teacher explained us a Ratherford model of atom and used some terms like "spin" and "quantic number". I'm havin trouble with these terms and maybe anybody can explain me the function of "quantic number" and spinnig and give me a basic example. I just visited some web...

hi, Do the addition of non-linear terms in action play any significant role in string theory?? if so, what is its significance in string cosmology? --- anuradha

Suppose I have some expression. The analytic terms in its expansion can always be found from the coefficients of the Taylor expansion. What about the non-analytic terms? Is there some systematic way to obtain them?

...than my current unit,is there danger that some component in my PC will be destroyed?

Homework Statement Define the following terms: a) Midpoint M of segment AB. b) Perpendicular bisector of a segment AB (you may use the term "midpoint" since ypu have just defined it). c) Ray BDbisects angle ABC (given that point D is between A and C) d) Points A, B, and C are collinear...

Ok, I am not the best man at math but would like to understand the principles behind these sciences. However these terms are really messing me up. Please someone out there help. 1.) Is there a difference between Quantum theory and Quantum Physics 2.) What is the difference between...

when we try to build the gauge theory of gravity we needs the vierbeins fields and spin connections fields. In the case we take them independent, which are the kinetic terms for two fields? or in other words, is the commutator of covariant derivatives the kinetic term for vierbeins and for spin...

I'm sure there's been a lot of posts on this before, but even after taking a look at some of them, this experiment is still eluding my understanding. I'm aware that there's no backwards causation--and that the eraser causes interference by random 'categorization'--but I'm nonetheless...

I am trying to deduce the expression for pressure of perfect gas when the momentum distribution n(p) is given. Here is how I did. First we assume a box with side length L_x, L_y, L_z, when a particle , say moving a long x direction, collide with one side of the wall, the total change of...

I realize my questions are very basic, that is because my background is a bit different, and I have to understand these terms to be able to do my work I guess all people here are famiilar with these basic things, please help me, I would appreciate your time ... what we mean if we say need to...

Homework Statement A body falls vertically from rest. During the nth second it falls a distance d. Prove that by the end of the nth second it has fallen a total distance (D) of (2d+g)^2/8g Homework Equations x = x0 + V0 + 1/2at^2 where x0 = initial position v0 = initial velocity a...

Homework Statement ST= 2TP. If \overrightarrow{TP}=a , \overrightarrow{PQ} = b and \overrightarrow {QR} = C express in terms of a, b and c a) \overrightarrow{RT} b) \overrightarrow{ST} c \overrightarrow{SR}...

It is known that \sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N I am looking for any asymptotic approximation which gives \sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ? where M\leq N an integer. This is not an homework

I'm not sure if this is the right place to post a graduate level course material, but I have a question about perturbative expansion of the 2n-point function of a scalar field theory. Homework Statement First, the question: In which space (position or momentum) is the topological distinctness...

my question and where i got stuck in the solution are in this link: http://img244.imageshack.us/img244/5316/84661104oi7.gif

Homework Statement Be x an element in the interval [Pi/4, 3Pi/4] express cos(2x), sin x, sin (x+pi) in terms of x. You must know that, for this question, cos x = z and z will always be < 0. Homework Equations cos(2x) = 2 (cos(x))^2 - 1 cos(2x) = cos^2 x - sin ^2 x sin^2 x + cos ^2 x = 1...

Homework Statement The function f is defined by y=f(x) = 3ln4x 0.01<=x<=1 a)Solve for x in terms of y and hence find the formula for the inverse function f^-1(x) b)Write down the domain of f^-1 c)Plot f from x =0.01 to x=1 and than plot f^-1 on the same axes but only for domain...

Homework Statement A block of mass m lies on a horizontal table. The coefficient of static friction between the block and the table is µs. The coefficient of kinetic friction is µk, with µk < µs. Suppose you push horizontally with precisely enough force to make the block start to move, and...

what type of lectures should i look for in order to understand this ?? i am taking a calculus course which involve them

Hi, I'm an industrial designer and I was wondering if there is a way to charge a battery through magnetic induction. I have heard that the way some stop lights work is there are coils below the road, and when the steel body of a car goes over it, it creates a change in charge in those coils...

If F=mg, and Fc=Fg, Fc=mv2/r (thats v squared; my apologies, i have no idea how to use the superscript button), and Fg=Gm(1)m(2)/r2 (squared), where m(2) is the mass of, say, the earth, and m(1) is the mass of the object orbiting the earth. By substituting these equations together, we get...

In Einstein's field equations, the pressure terms on the diagonal of the stress-energy tensor contribute like energy density to the "Komar mass", and help determine the curvature and hence the gravitational effect. I believe that these terms represent "rate of exchange of x-component of...

Homework Statement A basketball (which can be closely modeled as a hollow spherical shell) rolls down a mountainside into a valley and then up the opposite side, starting from rest at a height H0 above the bottom. In the figure, the rough part of the terrain prevents slipping while the...

If we have two charges, one at, say, 1C and one at, say, -1C, and they are separated by a distance of 1 meter, why is the voltage directly between them zero? A positive test charge will move towards the negative charge, and gain kinetic energy, but it started with no potential energy, and...

If x=cos(theta) how do you find what d/dx is in terms of d/d(theta)?

Consider a set that has integers p and inverses 1/q, infinitely many of both. We are about to form a product of all numbers in this set, with two different arrangements. Arrange terms, way 1: For each p (countably many), select 1/q so that q>p, the resulting product term is (p * 1/q) < 1...

I go to a smaller, teaching university, and do not have much opportunity for research at my own school. I do have one professor doing actual research and have been working with him for several semesters now. I also have had 2 REU's. To summarize my experience: 1. 2 REU's with the same...

What does "finite" mean in mathematical terms? I was reading a discussion on here about whether or not Pi is infinite. It seems intuitive to me that it's not, but I'm having trouble grasping the idea that it (or any other number) is finite. From what I understand, if something is finite...