Term Definition and 742 Threads

I have following topics and I have to choose one among them for the term paper in Calculus II: 1- Numerical Analysis. 2- Sequence and Series. 3- Polar Coordinates. 4- Finding Areas through Integration. What topic would make the most interesting paper considering the applications? P.S...

Homework Statement Find the complex Fourier series for f(t)=t(1-t), 0<t<1 Homework Equations \sum_{n=-\infty}^{\infty}c_{n}e^{2in\pi t} where c_{n}=\int_{0}^{1}f(t)e^{-2in\pi t}dt The Attempt at a Solution I've worked out that c_{n}=-1/(2n^2 \pi^2). The problem is that for...

Homework Statement This type of questions seems to be easy, but a little confusing at the same time If we are given the Sn of a series, and were asked to find an how to do that ? Homework Equations the limit of series and Sn is the same The Attempt at a Solution Maybe we...

What is the name of the theory (or person who thought it up) that the universe is infinite in the 4th spatial dimension and that our big bang is only a local effect?

hello there any body know Define the term ‘’discrimination’’, as applied to power system protection. im can't find if you can help me please thanks a lot

Homework Statement This should be easy but I can't find why. Why is the following true for 0<x<1, \lim_{n \rightarrow \infty}nx(1-x^2)^n = 0 Homework Equations The Attempt at a Solution I understand why (1-x^2)^n goes to zero, but the nx part is not bounded and seems to...

Homework Statement A man walks steadily outwards on a turntable (radius r) with radial velocity v. The turntable rotates with angular velocity w and angular acceleration alpha (anti-clockwise). What is the tangential component of acceleration? Homework Equations radial acceleration =...

Infinite Series without an "x" term What are the uses of an infinite series which does not include an "x" variable? If you are looking at an infinite series which sums terms based entirely upon each term's position in the series, or, a series which includes only the variable "n," how would...

√2, √(2√2), √(2√(2√2) ), √(2√(2√(2√2) ) ) this sequence has been giving me a lot of trouble. i have no idea how to write the fomula. please help me.

hi all,o:) anybody please give me a physical explanation for the Gauss-Bonnet invariant... What is its significance in cosmology??does it contribute to the late time acceleration of the universe?? is it possible to find the variation of Gauss-bonnet term with respect to any given metric?if...

I was given the following ODE to solve and it seemed simple enough. However, after you have used the integrating factor the integral is not integratable. y' = (1+x^2)y +x^3, y(0)=0 Find y(1) if y(x) is the solution to the above ODE. So I put it in the proper form of: y' + (-1-x^2)y...

Homework Statement Hi all. Please take a look at this expression, where T is our variable (it represents temperature): C_v = 2\left( {\frac{{\hbar \omega }}{T}} \right)^2 \frac{{\exp \left( {\frac{{\hbar \omega }}{T}} \right)}}{{\left( {\exp \left( {\frac{{\hbar \omega }}{T}} \right)...

Defining the term "connected" Some authors use the word "connected" as applied to a set S to mean that for any two points A and B in S there exits a (piecewise) smooth path in S from A to B. This is, for instance, the approach taken by Apostol in Calculus Vol II (p 332) and the approach taken...

Please help with Kinematics HAVE MID TERM TOMRROW :(! I have a mid term tomorrow and I'm in a dire situation. I don't remember how to do kinematics equations like A bus leaves the terminal and travels for 900s at an average velocity of 10 m/s before it stops at its first destination. How...

1. If you`re given an equation such as w(t) = (1+t)e^jt how would I go about graphing it. For different values of t i get a different complex number but how do I represent that complex number on a w(t), (t) axis?

when we apply Higgs mechanism to the lagrangian of a complex scalar field... we get terms for a Glodstone boson, a massive scalar and a massive vector field in the new lagrangian.. we also get other terms.. one of them takes following form A_\mu \partial^\mu \xi this term is said to...

Lambda is the quantum number for the total orbital angular momentum of the electrons about the internuclear axis. Unlike in atoms, the cylindrical symmetry created by the strong electric field of the nuclei in a linear molecule destroys the relationship [H ,L^2] = 0. Can anyone tell me...

[SOLVED] Why can't i cancel this term? http://tinypic.com/view.php?pic=2jcc49l&s=4 The function g(x) is stated in the first line. The question asks for g' when x=0 In the third line, i canceled e^x from both terms in the expression. The TA wrote that i can't do that. I forgot to ask him...

Origin of the term "seperable" I was just curious as to why out of all properties of metric spaces (ie compactness, closure, etc), i don't know how the term seperable makes sense intuitively... is there an origin to this term? Just curious. cheers

Hello! I've some problems understanding why in field theory a term (appearing in a Lagrangian) like \propto \phi^{2} is called "mass"-term (whereas \phi denotes a real field). Is there any interpretation? And is this a general expression for a mass term or could it be of any other shape...

The term "mutual" velocity, can be described as? Homework Statement A 110 kg tackler moving at 3.0 m/s meets head-on (and tackles) a 95 kg halfback moving at 7.5 m/s. What will be their mutual velocity in meters/second immediately after the collision?Homework Equations m1 = 110kg V01 = 3.0...

Homework Statement Find the coefficient of X^3.Y^2 in (1+2X+5Y)^6 The Attempt at a Solution This question would be much easier for me if not for the constant term inside the brackets. I seem to recall that the coefficients of expansion for functions such as (ax+by)^n can be determined...

Homework Statement Not really sure where tou go with this one. Homework Equations If the nth partial sum of a partial series is given by, Sn= \frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{2n} = \sum_{k=1}^{n}\frac{1}{n+k} a) write the associated series b) test for convergence c) if...

During my research a while ago, I have unexpectedly derived a "modified Dirac equation" with a \gamma_{5} mass term. (\gamma^{\mu}\partial_{\mu}+\gamma^{5}m)\psi(x)=0 I was quite surprised, and went about asking a few people. The answer I got is this equation is not new and has been...

Homework Statement (note: this is not an easy question and will be marked very strictly.) Find the values of the constant a and b such that limx->0 ((ax+b)^1/3)-2)/x = 5/12 NOTE: you are not allowed to use L'Hospital's Rules for this question Homework Equations whatever you learned...

Please help what term to use for the following issue. Given a set X = { x1, x2, ..., x_n } and a probability distribution on it P (X) = { p (x1), p (x2), ..., p (x_n) }. Given a division of the set Х on non-overlapping subsets Х1, Х2, ... Х_m, so: X1 U X2 U ... U X_m = X Is there a...

Hey guys, Homework Statement Solve the following DE, y"+t(y')^2=0I'm not sure what to do with the square there. Would it help if i divided the whole equation by y'? Thanks

Homework Statement The question is this: Expressing the kinetic energy in terms of momentum (K=1/2mv2 = p2/2m), prove using symbols, not numbers, that the fractional loss during the collision is equal to M/(m+M) Homework Equations The Attempt at a Solution I'm not sure where to...

i know that there is a formula to find the nth term. two questions: what does mean for non-integer n (as the recurrence relation breaks down i think), and how was this derived

Im learning math and physics on my own and I have had some problems when it comes to remembering how to do topics about math and physics. Currently I am trying to make more summaries, and a list of math and physics topics in order to remember more about them. Do you guys have any advice or...

I am reading a research paper about "narrow" autocorrelation and at the beginning there is an expression I don't unterstand http://www.wellesley.edu/Physics/brown/pubs/acv85_P1595-P1601.pdf" Does someone know what is meant with the word cross term?

A simple question. Suppose I have \epsilon^2 y''' - y' = \frac{1}{1+x^2}. The goal is to calculate the Fourier transform of y(x,t) where we define, \hat{y}(k,t) = F[\phi] = \int_{-\infty}^{\infty} y e^{ikx} ds We're also given that, F\left[ \frac{1}{1+x^2} \right] = \pi e^{-|k|} Now we...

Hi, Can anyone tell me an algorithm to generate the stationary Gaussian distribution R(t) with \langle R(t) \rangle = 0 (zero mean) \langle R(t) R(t')^{T} \rangle = A \delta(t-t') , A = 2 \gamma k_B T m (autocorrelation) ? What I just wrote is from the Wikipedia article "Langevin...

Homework Statement \int^1_0 \int^1_y sin(x^2) dx dy The Attempt at a Solution This equation cannot be integrated nicely, so I tried to reverse the order of integration: \int^1_0 \int^1_x sin(x^2) dy dx However this only helps for the first step, since when we intregrate by y, we...

Is "black hole" a racially insensitive term? http://blogs.chron.com/sciguy/archives/2008/07/is_black_hole_a.html July 09, 2008 Is "black hole" a racially insensitive term? Apparently to some. From the City Hall Blog at the Dallas Morning News: A special meeting about Dallas County...

Use of the term "pair" vs "ordered pair" Why is it that authors use the term "pair" and "ordered pair" interchangeably and, maybe I'm mistaken, a little imprecisely? For example, in listing the field axioms, the language "for every pair x and y" is usually used. However, surly the author means...

What does it mean when an algebraic variable has a dash above it? _ ---------------------------------------------------------------->z, like that?

I'd like to know how most mathematicians view the concept of set. When used in a context outside of set theory, does the word "set" take a meaning (as opposed to leaving it as an undefined term in a set theory) that does in fact follow the axioms of a complete set theory, and therefore all...

Who coined the term "relativistic mass" I asked this question before and never got an answer. I'm hoping that new people are on here who might just know the answer to the question: Who coined the term "relativistic mass" and where, i.e. I need a reference so I can read the source of the terms...

Hi guys...I am trying the problem 5.2 from Peskin to calculate cross section for Bhabha scattering. In the interference (cross) term, I'm getting a term involving trace of 8 gamma matrices and I am having some trouble in evaluating it. So can anyone help? The term is...

Homework Statement The nth term for a sequence is the square root of [n/ (n^4 + 1)] Investigate whether it is convergence or divergence. Homework Equations Ratio test and integral test The Attempt at a Solution Ratio test will fail for this question, since no conclusion can be...

For a problem such as \sum (1-3/n)^n with the sum going from 1 to infinity, the textbook shows to use the nth term test & that it diverges. However in a previous chapter the textbook had a theorem that said the limit of \sum (1+x/n)^n will converge to e^x for any number x. So I'm confused...

I'm looking for help with my conceptual understanding of part of the following: 1) If a series is convergent it's nth term approaches 0 as n approaches infinity This makes perfect sense to me. 2) If the nth term of a series does not approach 0 as n approaches infinity, the series is...

Ok i have a few here that i have no idea what to do b]1. Homework Statement [/b] Find the nth term in the series 1/2, 1/3, 2/9, 4/27, 8/81, 16/243 also \Sigma (-1)^n-1/ 5n+1 find the sum Urgent help neededdd ahha.. Thanks

[SOLVED] Double integral with cos(x^n) term Homework Statement Solve the following integral (without using a series development): \displaystyle \int _{0}^{\frac{1}{8}}\int _{\sqrt[3]{y}}^{\frac{1}{2}}\cos\left(20{\pi}x}} ^{4}\right)dx dy Homework Equations N/A The Attempt at a...

Can someone explain to me why different terms arising from a particular electron configuration have different energies? For example, for carbon in the configuration 1s^22s^22p^2 three terms arise, 3P 1D and 1S. These three terms have different energies but I don't understand why. The electron...

So I got a terrible result in my QM midterm. 17%... Fortunately, its only worth 20% of grade. Thing is I didnt really have time to study for it. I had so much other stuff, and figured Id get a B or C relying on what I learned doing problem sets. Boy was I wrong. I know I can still do...

Well my first semester in university went terribly, I just got by. I really slacked around and wasn't prepared for the workload. I have hopes of going to med school but I'm wondering if a really bad first year will have a big impact on getting in?

i added my question and how i tried to solve it in the link http://img100.imageshack.us/my.php?image=img8257ge1.jpg

I've been wondering about terms you typically find in the action of a field theory, for example consider the kinetic term of a scalar field S=\int d^4x(\partial_\mu\phi\partial^\mu\phi). I've read that it can be thought of as the kinetic energy of the field - but this just doesn't sit to...