What is Variation: Definition and 574 Discussions

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...

Im supposed to show that a ligth beam traveling in a vertical plane satisfies d^2z/dx^2=1/n(z) dn/dz[1+(dz/dx)^2]. Using calculus of variations to minimize the total time. The vertical plane got a refracting index n=n(z) there z is the vertical position and z=z(x) there x is the horisontal...

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 :uhh:. 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 pot to...

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...

Homework Statement Well, I think I could figure this out, but I have limited time, and apparently it isn't meant to be in THAT much detail. I'm attempting to assess how the volume of a balloon will vary with mass of gas added to it. It doesn't have to be exact. Homework Equations I'm...

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! :yuck:

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...

Nonhomogenous LODE (Higher Order) - Method of Variation of Parameters x^3y''' + x^2y'' - 2xy' + 2y = x^3log(x) y(1) = \frac{10}{32} y'(1) = -\frac{24}{32} y''(1) = -\frac{11}{16} I know that \inline y = y_h + y_p and that I probably should use the method of variation...

Given that http://forums.cramster.com/Answer-Board/Image/cramster-equation-200641003458632802260985487500893.gif is the complementary function for the differential equation http://forums.cramster.com/Answer-Board/Image/cramster-equation-200641003635632802261951581250765.gif use the variation...

Use the method of variation of parameters to find a particular solution of http://forums.cramster.com/Answer-Board/Image/cramster-equation-2006491914366328020687673812501253.gif ok i know first i do...

i've read in a website that cp variation is the possible reason for excess matter left over in the big bang, is that true can someone please explain the cp variation?? thanks

Today, March 20, "is the Vernal Equinox". This event seems to vary yearly between the 20th and the 22d of March, without any obvious pattern. And I wonder if there is any clear description of the relevant variables that cause the variation. I am not iterested in a formula to calculate it...

I'm not currently in a class, but I'm doing this for fun.. but technically I would still call it coursework, so I'm posting it here.. I'm studying Redheffer/Sokolnikoff's Mathmatics of Modern Engineering.. and I find a problem on page 75, use the method of variation of parameters to find the...

Hi all! I started my first control engineering course this semester. There are some terms that confused me. I am now learning closed-loop systems. And the lecturer was discussing the reduced sensiticity to process disturbance and load variation of a closed-loop system when compared to a...

OKay everyone, this is a big f'ing problem (to me anyways) and its only worth 1 point! But I'm doing it anyways. So here was my attempt, everything seems to be working out like it should but look at what u1 came out too, what am i going to do with that mess? Also do u see any mistakes...

OK, so I'm pretty familliar with the regular twin paradox and the explinations of how you decide which twin is younger by noticing which one accelerated, and the geometrical view of this using k-calculus and minkowsky diagrams, etc. I just thought of something though, and I guess my relativity...

First of all I have put in ALOT of research into this and I do realize there is no standard formula for the variation of B with the distance because the configuration/polarities and so on tend to get complicated. However, part of my investigation involves measuring the variation of the...

i haven't yet got this concept. i have read about the time "freezing" near a BH , but am not clear. can u please explain what actually happens? why does the time stop? i also want to know one thing-- when, supposing 'A' enters the event horizon he moves slowly towards the singularity because of...

I don't have access to textbooks. The internet at present is pretty much my only source of information. I tried looking on the net but couldn't find anything pertaining to my questions. Ok so I have the expression for a Poincare invariant action. Then I have to find the variation of the...

If I have the expression for a Poincaré invariant action, how do I find the variation of the action? Any help/hints much appreciated, thanks ;)

i'm confused about that method: 1) when proving that method works, why do you have to make u and v satisfy the 2nd condition u`y1+v`y2=0 2) when you're integrating to find yp, why do you leave out the constant that results from the integration?

I know how to solve the following ODE with variation of parameters: y''+4y=4\sec{\left(2t\right)}. Is there any way to solve this with undetermined coefficients? So far I have tried Yp=Acos(2t)+Bsin(2t), but that didn't work. Thanks for the help.

Consider the following situation : There are three variables A, B and C. (and i,j,k are constants ) Keeping C constant, and varying the other two, you find that A = kB ------(1) Now, Keeping B constant, and varying the other two...