Variation Definition and 540 Threads

As I understand it, a tesla turbine runs by injecting steam, or some other gas onto the outside of several disks mounted parallel to each other on a shaft. The gas is directed roughly tangent to the outside of the disks and it exits through openings in the center of the disks. Seems straight...

EDIT: Sorry... I have to use perturbation theory. My mistake. Hey... I have a quick question. I have to calculate the approximate change in energy via variation theory when the 'error' Hamiltonian for the Stark effect is defined as: |\vec{E}|cos\theta\bullet eR If I'm not mistaken, the change...

After the "I DERIVE YOU" math joke (posted somewhere in the stickys) Here is one having a similar punchline, but, in my son's opinion, with a MUCH better joke: A constant function and an exponential function are walking down the street and they see a partial derivative. "Go over and talk to...

Sorry about twin paradox again, I'll try to keep this simple as simple as I can. Initial situation: All participants are at rest, A1 and A2 are together at midpoint between B1 and B2. All clocks are in sync. _____________A1, A2 _____B1____________________B2 ---- A1 and A2 move...

Homework Statement Give examples of methods used to find approx. answers to the Schrödinger's eqn. of systems too complex to be solved analytically. Homework Equations None required. The Attempt at a Solution I understand there are three methods commonly used, those mentioned in...

[SOLVED] Variation of Parameters Homework Statement y^(4)-6y^(3)=-5sinx The Attempt at a Solution I factored this at x^3(x-6)=0 so my r values are 0,6 also using for y(p) Dcosx + Esinx y=Ae^0 + Be^6x + Dcosx + Esinx ? y' =6Be^6x -Dsinx + Ecosx y'' =36Be^6x-Dcosx - Esinx...

Homework Statement Okay so when solving a system of D.E.s using Variation of Parameters I know that first I find the complementary solution Xc and then do a bunch a of crap after that using the fundamental matrix. Now I just came across a problem with repeated roots, so I just want to...

So I pretty much have this Differential Equation solved except that I have to integrate the expression \int \Phi(t)F(t)dt it has a star next to it in my attached work. Does this look readily integrable to anyone? For some reason nothing is ringing a bell. I suppose I could go by parts, but...

Recall that some traits, such as skin color, appear to be controlled by several genes. This creates a continuum of variation. If this polygenic explanation for the inheritance of human skin pigmentation is correct, how do the skin colors of the following 4 individuals compare? Which of the...

Hi, Here's the problem: Homework Statement Quantum particle moving in 1D. Potential energy function is V(x) = C|x|^{3}. Using the variational method, find an approx. ground-state wave function for the particle. The Attempt at a Solution Using \psi = Ae^{-ax^{2}}, I find that A =...

FTL Signaling with Dopfer - Why Won't This Work? I think at the outset we will all agree that the following will not work, but the more interesting question will be why. Take the Dopfer experiment described at: http://www.quantum.univie.ac.at/publications/thesis/bddiss.pdf On page 36...

Solve by method of variation of parameters (x^2)y'' - (4x)y' + 6y = x^4*sinx (x > 0) Hey, I know how to solve problems using variation of parameters but only when the corresponding homogenous equation has constant coefficients... y'' - (4/x)y' + (6/x^2)y = 0.. the bit I am confused about...

I read on NIST CODATA that electron mass is a fundamental constant. I take from this that proton mass is not fundamental. I also read it is possible that proton-electron mass ratio may vary. So I wonder how proton mass is measured or derived. I have no training in physics, however in studying a...

Homework Statement Use the method of variation of parameters to determine the general solution of the given differential equation: y^(4) + 2y'' + y = sin(t) Homework Equations characteristic equation is factored down to (r^2 + 1)^2, so r = +/- i. this gives the general solution to be...

Homework Statement Suppose a function Aexp([-cr]^{2}[/tex]. To find optimized value of c, using variational method. Relevant equations[/b] The Attempt at a Solution I even don't understand how to start doing it. Is their anybody who can help me?

"What your favorite variation of" : Euler's Formula I generally find that mathematicians always have a preferred way of writing an expression, whether be it because to them it's more aesthetic pleasing or easier to memorize. Few expressions, however, lend themselves to many forms as thus...

Within the description for the variation of parameters procedure is the restriction: y1u1' + y2u2' = 0. Can you explain this restriction, it is not obvious to me, I do not have an explanation where this comes from. Is it related to u[ \frac {dy}{dx} + P(x)y] = 0 from solving first...

Greetings, Regarding the two procedures: undetermined coefficients and variation of parameters, can both procedures be used interchangeably - meaning they both solve (non-homogeneous linear equations)? Does one method work better in certain situations, if so which method is preferred when...

I always like to do the variational calculations in rigor way for example like this 0 = D_{\alpha} \Big(\int dt\; L(x(t)+\alpha y(t))\Big)\Big|_{\alpha=0} = \cdots because this way I understand what is happening. However in literature I keep seeing the quantity \delta x(t) being used...

Anyone know a good site to check up on how the star algol varies in brightness and how long its average cycle is?

I found a statistics question and am wondering how its figured out, the way its worded is hard to understand what everything means. anyhow.. If a coin is flipped N times, one expects to get "heads" roughly half the time. More precisely, Number of heads=N/2+Δn where Δn is the statistical...

Well, i really i am pissed at the moment because of this. I have been trying to figure out if there is a proof/justifaction for the method of variation of parameters and have had absolutly no luck. I have searched the internet and almost every differential equation books in my university library...

A variation of the double-slit experiment--myth or did somone really do it? I've heard this experiment described at least three times; possibly more. However, none of the sources are terribly reliable--Scott Adams in the last chapter of The Dilbert Future (and he freely admits that he gets a...

Homework Statement "If the circumference of a circle changes by a factor of 3, then its area changes by a factor of ____." Homework Equations C=2*Pi*r A=Pi*r^2 The Attempt at a Solution I really don't know where to start.Recently I have been learning about the changing of factors and I'm...

I put this question in the 'Calculus' forum but didn't really get a response. Maybe it's a silly question but I thought I'd try here anyway: Older textbooks on the Calculus of Variations seem to define the first variation of a functional \Pi as: \delta \Pi = \Pi(f + \delta f) - \Pi...

Older textbooks on the Calculus of Variations seem to define the first variation of a functional \Pi as: \delta \Pi = \Pi(f + \delta f) - \Pi (f) which looks analogous to: \delta f = \frac {df} {dx} \delta x = lim_{\delta x \rightarrow 0} (f(x+ \delta x) -f(x)) from...

How does the summer solstice affect the position of Hadley cells? I know that the solar equator is 23.5 degrees North, which differs from the 0 degrees (as a solar equator) for the equinox. For the equinox in the N. hemisphere, there are three Hadley cells, or cells of circulation. The range of...

Homework Statement x^2y''-2xy'+2y=x^3cosx Find a general solution by using variation of parameters 2. The attempt at a solution I already solved this one, but I have 4 questions: 1. I found the solutions x and x^2 to the homogeneous equation by inspection. Is this the only way to...

Sex cell? Quick question: Does every sperm cell in a male testicle contain the same genes, or can some sperm cells contain different genes, even though they are from the same person?

Homework Statement Let f_n, f: [0,1]\rightarrow \mathbb{R}, and f_n(x)\rightarrow f(x) for each x \in [0,1]. I need to show the following two things: a. T_0^1(f)\leq \lim\inf_{n\rightarrow \infty} T_0^1(f_n), and b. if each f_n is absolutely continuous and T_0^1(f_n)\leq 1 for each...

I have a problem which is basically a variation of the coupon problem... I can't get my head around it as I haven't done much stats :rolleyes:. I have a sample size of 900, say a pot of 900 balls, each with a unique id. Each week I am going to select a set number of balls randomly from the...

Homework Statement I going thorough some of my old notes and I saw this question for a proof. If f is linear function but not a direct variation and not the constant function 0, then for every pair of real numbers a and c f(a + c) not equal to f(a)+f(c).Homework Equations y = mx ( a...

Homework Statement Given that y=x^2 is a solution to the differential equation: (x^2)y'' + 2xy' - 6y = 0 <--- Eq.(1) find the general solution of the differential equation (x^2)y'' + 2xy' - 6y = 10(x^7) + 15(x^2) <--- Eq.(2) Hence write...

Hi, I have 2 little questions and hope to find some clarity here. It concerns some mathematics. 1) Is the variation of the metric again a tensor? I have the suspicion that it's not, because i would say that it doesn't transform like one. How can i get a sensible expression then for the...

Calculate the period of the Earth's moon if the radius of orbit was twice the actual value of 3.9 x 10^8 m. a. 1.13 x 10^6 s or 13 days b. 2.3 x 10^6 s or 26 days c. 5.14 x 10^6 s or 59 days d. 6.85 x10^6 s or 79 days So far I got: v=velocity; T=time; h= hieght from surface v=? T=...

Homework Statement Hey guys, I'm helping my girlfriend who is in a 101 physics class...ha, I've taken enough engineering physics, and I guess I can't figure this one out. I'm thinking too much into it, and can't even understand the question(what its asking). Is there a pressure...

Homework Statement Right, the problem is of course to sketch a graph of velocity against distance in an electric field. the second part, drawing the grapgh with an electric field opposing the motion of the electron. The Attempt at a Solution Right, assume we have an electron. We...

Chris Hillman mentioned something in the engineering forum recently that piqued my curiosity: https://www.physicsforums.com/showthread.php?t=149937 Some questions came to mind: Do males really vary more in traits than females? Which traits? Is this true for most species? What explanations...

In the "buffons needle" riddle you have a paper with horizontal lines in it all 1 unit apart and you drop a needle 1 unit long - you have to calculate the chance that the needle will hit a line. but i remembered the riddle wrong so instead i tried to solve the same question with both horizontal...

Let be a functional S so \delta S =0 give the Euler-Lagrange equation where: S= \int_{a}^{b}dtL(q,\dot q, t) My question is ..How the "second variation" \delta ( \delta S )=0= \delta ^{2} S defined??.. in order we could decide if a function q=q(t) is either a maximum or a minimum...

anyone can help me out by providing the mathematical relationship between yield strength and temperature

Find variation - really need help! guys i really need your help on this. I don't even know which section to look for here. can some one please get me started for this problem. Problem: A manufacturer contracts to mint coins for the federal government. how much variation dr in the radius of...

Hi i need to use Variation of Parameters to solve this ODE x^2 y'' - 2xy' + 2y = x^(9/2) So far I was thinking to use Euler's Equation and I really don't know if it will work please help me out with a hint. THanks.

hey guys, only my second post here, hope these boards are helpful! I have a problem for my fluid mechanics class and was wondering if anyone could help me out. i will post the question and the figures and what assumptions i have made due to the lack of information. Several holes are...

When an observer stand on at the place with a angle "a" of the latitude, the observed value of the gravity will be affected by the motion of the rotation.SO what is the value of the obversed gravity at that time?

Based on the proof given in the action article of wiki (http://en.wikipedia.org/wiki/Action_%28physics%29#Euler-Lagrange_equations_for_the_action_integral), it would seems that the statement of the "central thm of calculus of...

can anyone help me? Desperate! What are the CURRENT development of calculus of variation that has impact on our society? Like in the area of engineering, I.T. etc?? And can anyone provide me a webby on that please thank you!

Hi all, I'm a maths and physics student from college. I have been asked by tutor to make a small report on the uses of calculus of variation which has an impact of society... I have been searching up and down but can't find anything specific or easy enough to understand on the internet.. I was...

Calculus of Variation (pls help!) hello! can somebody explain to me what's calculus of variation?? and more importantly, how it is applied in everyday life (such as consumer's products, industries etc) ? :) thanks so much! :!) really really need help!

First of all if you read this and the latex is all messed upp I am probably working on getting it right so please be patient till I get it right. No need to post a comment that it doesn't work. Thanks :wink: I haven't taken a pure maths class in over 2,5 years so I can hardly remember how to...