Term Definition and 742 Threads

"Find the next term" After studying more math, I've been conflicted about this type of assignment commonly given to high schoolers. In the sequence 1, 4, 9, 16, ____ find the next term. On one hand, it's a good exercise and teaches pattern recognition. On the other though, it seems to go...

Reading over Alcubierre's paper on his "warp" drive (http://arxiv.org/abs/gr-qc/0009013), the metric in equation 3 has a velocity term, v, that doesn't seem to be needed anywhere. Even in the one spot where it seems potentially valuable, equation 12, he just call it =1 and essentially ignores...

Homework Statement I've done physics in a non-english medium and I want to know what is the technical term to call the incident where the image is flipped vertical through a mirror. I mean if we stand infront of a mirror and raise the right arm, the mirror image shows we're raising the left...

My first post, and a very long one... I have problems understanding the prolific use of a certain term in the rocket thrust equation and its validity. The general rocket thrust equation contains a term referred to as the pressure thrust. It is calculated as (p_e – p_a)Ae where p_e is the...

Imagine a straight line that contains both the center of the sun and the center of the earth. This line passes through a point on the surface of the Earth that is between those two points. As the Earth rotates, this point moves west, forming a kind of line on the surface of the earth. What...

Ok so i have the equation y'=y^2(y-3)(y-5)^3 I found the equilibrium positions to be y=0, y=3, y=5. For my phase diagram all the arrows are pointing up so the solutions are nodes? The last part asks Describe the long term behavior of the solution to the above differential equation with...

Hello to everyone, I urgently need to solve the following pde: ∂u/∂t +∂²u/∂x² = So*δ(x-xo)*sin(wo*t) It's the heat equation with a cyclic source. The lentgh of the cable is L. I have no clue how to do this with such a source, all i have learned was to do a separation of variables, but it...

I will be graduating with an engineering degree (mechanical) in May of 2014. The city that I currently live in is not where I want to stay after I graduate; however, my wife is well established in her career and it makes sense for us to stay here for a year or so in order to save up money etc...

Dear Forum, Does every sequence have a general term? What is the definition of the general term of a sequence? Best wishes

I'm trying to clarify for myself the relation between the stress-energy tensor and the mass scalar term in metric solutions to Einstein's equations. Maybe I should also say I'm trying to understand the energy tensor better, or how it relates to boundary conditions on the solutions. My...

First of all, I'm not sure if this thread belongs here or at the "Special & General Relativity" sub-forum, if I posted at the wrong place please move it. Homework Statement I encountered this problem working in my master's degree. I need to find the stress-energy tensor of the following...

Homework Statement combustion adds 1200kj/kg to the charge. what is the meaning of " charge" here. Homework Equations The Attempt at a Solution

Hi everyone, I'm reading Logic for mathematician form A.G. Hamilton, at some point the book explain what a free term is, but I'm not sure how to determine if t is free or not. I was wondering if one of you may have a link where I could read more about it. (I have find some info on wikipedia...

I have a question why is $$\frac{2x^2-1}{x^2+1}$$ equal to $$2-\frac{3}{x^2+1}$$ ??

In the context of my work (linear differential equations), it can not be zero. But why?

Homework Statement Approximate the value of the integral of 6/(1+2x) with respect to x from 0 to 2. Use 4 subintervals of equal width and use the left endpoints. Homework Equations delta x = (b-a)/N The Attempt at a Solution The integral is the sum of 6/(1+i) from i = 0 to i = N-1 or 3...

Homework Statement Let ##\displaystyle a_n=\frac 1 2+\frac 1 3+...+\frac 1 n##. Then A)##a_n## is less than ##\displaystyle \int_2^n\frac{dx}{x}##. B)##a_n## is greater than ##\displaystyle \int_1^n\frac{dx}{x}##. C)##\displaystyle \lim_{n\rightarrow \infty} \frac{a_n}{\ln n}=1##...

I have to solve a bunch of exercises related to function series and in some of them they ask me whether a particular series converges uniformly if one differentiates it term by term. So here I came up with a doubt: When ##\sum_0^{\infty} f_n(x)## can be differentiated term by term? What...

We used to classify signals as 1D and 2D etc ie one dimensional and two dimensional. For example a periodic square wave signal is 1D and an image is a 2D signal etc (reference - Signals and systems by Simon Haykin and Barry Van Veen, 2nd edition , page 2). But the same periodic square wave...

In signal processing , what do the term 'feature' means? Feature extraction etc. For example, in audio signals what are the main features? -Devanand T

Origin of the term "chair" in academia? When I was very young, I wondered why professors (heads of departments) were said to have a "chair" in such-and-such subject. I thought of the story about King Louis XIV of France who was said to have a chair in (their equivalent of) the cabinet room...

Homework Statement I have two questions 1.Today,in my test paper,I got this sequence. Find the nth term formula 1,3,15,61,253 I didn't know how to start.This is clearly not an arithmetic or geometric sequence. Any help? 2. And is there any formula for finding the nth term of sequences...

Hi, I am trying understand if there is a quick way to figure out the impact of the X term in a quadratic equation. For example, by looking at the following equation, I know that it is a parabola (X^2) ; by looking at 24, I know that it is the y-intercept. However, I don't know what is the...

Google hasn't been very helpful on this one and my textbook once again assumes we are born with certain knowledge as it doesn't delve any further than, "Many practical engineering problems involve systems acted on by impulsive forcing terms" without further explanation. Isn't that nice... So...

Hello, This is not a homework, just trying to solve the previous exams and I'm stuck at one of them : Homework Statement Consider Fn(x)=1/(2*pi) * [ sin(n*x/2) / sin(x/2) ] Calculate: ∫ F2012(x) from -pi to pi Homework Equations The Attempt at a Solution I've tryed...

Solve the differential equation (5x+4y)dx+(4x-8y^3)dy=0 So M(x, y) = 5x+4y and N(x, y) = 4x-8y^3 Check \frac{\partial M}{\partial y} = 4 and \frac{ \partial N}{\partial x} = 4 check passed. f(x, y) = \int M \partial x + g(y) = \int 5x+4y \partial x + g(y) = \frac{5x^2}{2} + 4yx + g(y)...

Hello, could somebody please explain to me why in 4 of these solutions, the angular momentum final term about point p is mVfR + Icmω ? It is in huge attached solutions my teacher posted. Thank you very much in advance Here is the problem in case you are interested of Horne context. 4. A...

Can the term "distortion" be used interchangeably? Clipped sine wave = distortion Assume I run a 30hz tone through one of my dedicated mid-range loudspeakers. There's no doubt that the loudspeaker would bottom out. People often call this distortion. But the signal never clipped. It's the...

Hi, I'm trying to solve the flow profile inside an inhomogeneous porous material between two parallel moving plates (essentially Couette flow with a deviation), and I model my system by the following equations: \nabla^2 \mathbf{u} = p(x,y,z) \mathbf{u}\\ \nabla \cdot \mathbf{u} = 0...

term “scattering” more of a general process Is the term “scattering” more of a general process which incorporates the linear effects of reflection, refraction and diffraction?

Homework Statement I'm having a brain fart, how do you factor/simplify a fraction such as \frac{ab}{ab+cd} I keep thinking multiply by ab-bc but I'm not sure.

Is there a term to describe the phenomenon that observation seems to effect the outcome of superposition?

How exactly do you derive it without using tensors? You use Newton's frictional law on a 3d block of fluid, instead of just on fluid surfaces, but I can't 100% visualize how. So is there any simple derivation, or at least explanation? \mu \nabla ^2 \vec{V}

Like the topic,if in my system derivation, there is an independent gravitational force independent of the state variable, is my system linear? I believe it is not but my instructor is telling is it is. I'm thinking that if there is is an extra gravitational term,the output of the system does not...

The fibonacci sequence can be defined as $${F_n} = {F_{n - 1}} + {F_{n - 2}}$$ and specifying the initial conditions as $$\eqalign{ & {F_1} = 1 \cr & {F_2} = 1 \cr} $$  Also there exists a general formula for the fibonacci which is given by $${F_n} = {{{\varphi ^n} + {\psi ^n}} \over...

Solve the differential equation by separation of variables x \frac{dy}{dx} = 4y becomes \frac{1}{4y} dy = \frac{1}{x} dx Integrate to get \frac{1}{4} \ln{|y|} = \ln{|x|}+C I'm stuck here because I want to raise e to the power of both sides of the expression like e^{ \frac{1}{4} \ln{|y|}} =...

I've been thinking about chapter 11 of Griffiths' Introduction to Elementary Particles. In section 11.7, he gives the Lagrangian density \mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)+\frac{1}{2}\mu^{2}\phi^{2}-\frac{1}{4}\lambda^{2}\phi^{4} and shows that the minimum...

Here is the question: I have posted a link there to this topic so the OP can see my work.

I have two questions having to do with the Lorentz transformation for the time...some preamble first: The Lorentz transformation for time along the x-axis is t'=\frac{t-\frac{ux}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}, where u is the relative velocity of S'. Why is there a dependence on x...

Hello! The following system of linear equations has been expressed in term of column vector in the following. . How can I express the system of linear equations in term of row vector? In addition, What is the field of scalars? I would request to explain it. Thanks in advance.

Whenever I ask someone what an electromagnetic field is exactly, they say that science does how questions, not why questions (which doesn't really make sense in this context, maybe i worded my question differently). We say that there are four fundamental forces that create the universe we live...

After multiplication the coef. of x2n was found which is highlighted in red in the paint document. My question is, is there an easy way of finding the coef. without actually going through the process of squaring the series given and locating the pattern for the coef. for x2n? What I tried...

When I first learned time dilation I was given this equation proven using the light clock example. t = γt' However, when I looked into the topic in more detail, I was given this equation. t = γ(t' + xv/c2) If x represents the distance between 2 frames, then does x have to change...

Homework Statement A bored student enters the number 0.5 in her calculator, then repeatedly computes the square of the number in the display. Taking A0 = 0.5, find a formula for the general term of the sequence {An} of the numbers that appear in the display, and find the limit of the sequence...

A sequence of positive integers is defined as follows: The first term is 1. Then take the next two even numbers 2, 4. Then take the next three odd numbers 5, 7, 9. Then take the next four even numbers 10, 12, 14, 16 and so on. Find the nth term of the sequence.

Hi. I'm having some difficult in understanding something about the dipole term in a multipole expansion. Griffiths writes the expansion as a sum of terms in Legendre polynomials, so the dipole term in the potential is writen \frac{1}{4 \pi \epsilon r^{2}}\int r^{'}cos\theta^{'}\rho dv^{'}...

How can there be a term called "intestinal metaplasia" of stomach Hello everyone, Ok Stomach's normal epithelium is simple columnar, now in intestinal type of adenocarcinoma of stomach it undergoes "intestinal metaplasia", due to gastrititis. Now intestine also has simple columnar...

How to find nth term of the sequence 6+13+24+39+...

I am a slow learner and I prefer to spend lots of time on few subjects rather than to distribute time over many. In addition, most of my courses will be extremely time consuming. So I probably want to take three courses per term and I will most likely attain a much higher GPA in this way, but I...

I am working through an example of an inverted pendulum on a cart, exactly like this: L is the length of the massless pendulum arm. Two degrees of freedom, x and theta. If I write out the kinetic energy as three parts: translational KE from cart + translational KE from pendulum +...