Variation Definition and 540 Threads

I am reading about a branch of mathematics which does not allow separable spaces. The author of the text gives the space of functions of bounded variation as an example of a non-separable space, which is fine - except for the fact that he goes on to claim that "this space is relevant to both...

Homework Statement 4y'' + y = cosx Solve using variation of parameters Homework Equations The Attempt at a Solution from a) -> yc(x) = c1cos(x/2) + c2sin(x/2) let y1 = cos(x/2) , y2 = sin(x/2) y1y2' - y2y1' = 1/2cosx/2 + 1/2sinx/2 = 1/2 u1' = ? How do I find this?

1.Homework Statement We know the derivation of the method of variation of parameters for second order scalar differential. The task is to derive the method of variation of parameters for scalar equations using this approach: first convert the scalar equation into the first order system and...

The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...

Homework Statement Hello, i have a small problem regarding this questions, If the function vs(t) is a function for t>=0, i can solve thus no problem (we are required to solve using variation of parameters). now i have a small problem, its not about how to solve it ,but how to approach...

Here is a brain teaser I came across recently. Ten prisoners are arranged single file in a line. They are sorted so that the shortest prisoner (prisoner #1) is in the front, and the tallest prisoner (prisoner #10) is in the back. The are all looking forward (in the direction of #1). They...

I've fabricated a simple half-wave microstrip resonator with gap-coupled microstrip feed lines. It's designed to operate around 10GHz, but due to slight over etching, the half-wave portion is 5-10um shorter than I intended. What might be more significant is that the gap, which was originally...

Homework Statement Find a particular solution using variation of parameters. y'' + 3y' + 2y = 4e^x Homework Equations yp = -y1 * INT (y2f(x)/W[y1,y2]) dx + y2 * INT (y1f(x)/W[y1,y2]) dx The Attempt at a Solution So, first I find the homogeneous solution, correct? r2 + 3r + 2 = 0, so...

Homework Statement A particle is moving in a simple harmonic oscillator potential V(x)=1/2*K*x^2 for x\geq0, but with an infinite potential barrier at x=0 (the paddle ball potential). Calculate the allowed wave functions and corresponding energies.Homework Equations I am thinking that the...

Homework Statement What do you do if one of the roots to the characteristic equation of a differential equation is zero when using variation of parameters? Homework Equations The Attempt at a Solution The problem I encountered this in is y" - y' = 4t Characteristic equation r2 - r = 0 so...

We know, in optics Fermat's principle is written in analogy with principle of Maupertuis in Classical mechanics (given by \delta S=\delta\int\vec{p}\cdot d\vec{l}=0). In terms of the wave vector it is written as \delta\psi=\delta\int\vec{k}\cdot d\vec{l}=0. Here \psi is known as eikonal (or...

Hi all, I'm going to ask a naive question - hope that's ok. There's been a lot of recent discussion of the results from Webb et al. which indicate that the fine structure constant varies spatially. I realize the results are very controversial - I'm wondering, hypothetically, if these...

Homework Statement s varies directly as r and inversely as t. s=10 when r=5 and t=3. What value of t will s=3 and r-4? Homework Equations Direct variation: y=kx; Indirect variation: y=k/x The Attempt at a Solution I tired s=kr=k/x and plugging in the given, but I could not get t in the end. My...

Hi, I was solving the following second order ODE: http://www.texify.com/img/%5CLARGE%5C%21x%5E2%20y%5E%27%27-5xy%5E%27%2B5y%3Dx%5E6%20sinx.gif I used variation of parameters and found this solution...

Do know anybody explicit form of variation action quadratic in Riemann tensors (for general dimension)? Link to internet sources? Or computer program for symbolic and tensors algebra, which the variation tell me (preferably open-source)? Thx

Homework Statement If y varies inversely as the square of x, and y = 1/8 when x = 1, find y when x = 5. y = 8/25 y = 1/200The Attempt at a Solution The equation to find this is y=k/x, I know that. I've tried to plug in both given answers to see which ones matched but neither of them did...

Background: Math: An affine parameter provides a metric along a geodesic but not a metric of the space, for example between geodesics. A connection provides an affine parameter, and a non-trivial connection gives rise to Riemann curvature. Given the existence of a connection with Riemann...

Imagine the setup of the original Schrodinger's Cat; The cat is behind the wall, locked. I am adding another element to it, a person that will enter the room without the knowledge of the experimenter, and exit through another door and seal the place again. So for the Observer unaware of this...

I conducted an experiment involving a 555IC timer circuit and the hypothesis investigated the frequency and period of the LED connected. Using the formula for frequency; 1.44/(Ra + 2Rb)C where R1= 1000R R2= 10000R C = 10uF the frequency equals 6.857 (rounded value) now using data...

Hi all, this will be my first physics qns:D more to come... I just learned that value of g at the equator is not exactly equal to the gravitational field strength. Can anyone explain with workings? i don't really understand my teacher workings. Also can i clarify if -We're assuming Earth...

hey, i am trying to find what is the process going on in the conductor while conducting ac. what is happening to electrons? what is the physical meaning of negative voltage in sin curve?

http://www.cdeep.iitb.ac.in/nptel/Mechanical/Heat%20and%20Mass%20Transfer/Conduction/Module%202/main/2.6.3.html" Kindly see the above link I will be placing a temperature sensor in the hollow area and insulate the outer surface(with let's say Plaster of paris)...I will place a fire...

Hey, I'm doing some examples in QFT and I don't want to go too far with this one: Doing gauge symmetries, we first introduce the Unitary spacetime-dependent gauge transformation that gives us a gauge potential. With the new gauge added Lagrangian, I want to take its variation to confirm the...

So I'm planning a senior honors thesis that'll start next summer. In my last post, I talked about testing magnetoreception, which is kind of risky. Another idea of mine is to take human subjects into a dark room, use filtered light to produce light at increments one 1 nm, and note the longest...

A ambiguous variation of Einstein--Hilbert action Variation of EH action is: \delta S_{EH}=\int_{\Omega}{\delta(R\sqrt{-g})dx^4}= \int_{\Omega}{G_{\mu\nu}\delta{g^{\mu\nu}}\sqrt{-g}dx^4}=0, where G_{\mu\nu}:=R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R is symmetric einstein's...

Title should read "Combining", is there anyway a moderator could alter that so the search function isn't messed up? Homework Statement The Attempt at a Solution I am familiar with both methods, however combining the two is foreign to me. Anyone have any suggestions for this ODE? My...

Homework Statement You are given that two solutions to the homogeneous Euler-Cauchy equation x^2 \frac{d^2}{dx^2}y(x) - 5x \frac{d}{dx} y(x) + 5y(x) = 0 y1=x, y2=x^5 y''-\frac{5}{x}y'+\frac{5}{x^2}y=-\frac{49}{x^4} changing the equation to standard form use variation of parameters to find a...

hi, I have to calculate total variation of this function: 1 for x< 0 sin(pi * x) for 0<= x <= 3 2 for x> 3 I could not find any example for doing this. Can someone help me ?

Hi, I have a 480 V, 200 kVAr and 60 Hz capacitor bank. I need to move this bank to a location with 390 V and 50 Hz, I wonder what would be the resulting power of the bank. Regards.

how does specific heat of gases vary with temperature? is there an equation to describe it?

Central Limit Theorem Variation for Chi Square distribution? If this question fits into Homework Help, please move it over there. I'm not too sure. I encountered the following problem: Now, this problem seems fairly similar to a simple proof the central limit theorem. I am damn sure...

Homework Statement Find the particular solution to the differential equation using method of variation of parameters: 4y''-4y'+y=16e^(t/2) The Attempt at a Solution Set 4y''-4y'+y=0 then the homogeneous solution is: y= c1*e^(t/2)+c2*te(t/2) set y1= e^(t/2), y2= te^(t/2)...

Homework Statement A rectangular tank is filled with water 2 m deep. At the bottom of one side wall is a rectangular hatch 1 m high and 2 m wide that is hinged at the top of the hatch. a) Determine the force the water causes on the hatch. b) Find the torque caused by the water about the...

Homework Statement t^{2} * y'' - 2y = 3t^{2} - 1 y_{1} = t^{2} y_{2} = 1/tHomework Equations Variation of Params forumla wronskian det The Attempt at a Solution W = t^2 * -t^-2 -[1/t * 2t] = -3 Y = -t^2 * Integral[ (-1/3)(1/t)(3t^2 -1)] + 1/t * Integral[(-1/3)(t^2)(3t^2 -1)] I get an...

I have a question on the integration part of the Variation of Parameters. Given .y''+P(x)y'+Q(x)y=f(x) The associate homogeneous solution . y_c=c_1y_1 + c_2y_2. The particular solution . y_p=u_1y_1 + c_2y_2. u'_1 = -\frac{W_1}{W} = -\frac{y_2f(x)}{W} This is where I have question...

Homework Statement y''+25y=cot(5x) Find one possible solution The Attempt at a Solution I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed). Ok, so I take...

4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?

Homework Statement Using variation of parameters, find the general solutions of the differential equation Homework Equations y''' - 3''y + 3y' - y = et / t where et/t = g(t) The Attempt at a Solution I know how to solve these types of equations when its a second order, but I don't...

Hey guys, This is my first post on PhysicsForums; my friend said that this was the best place to ask questions about math. Anyways, I have to find the Quadratic Variation of a Poisson Process. My professor doesn't have a class textbook (just some notes that he's found online), and...

1. Show that the variation of pressure with altitude for a planetary atmosphere (assuming constant temperature) is more accurately given by: p = poek(1/r-1/R), where g is taken to vary as 1/r2 (with r being the distance from the centre of the planet), po is the pressure at the surface, R is the...

I was doing some reading and I came across this: http://en.wikipedia.org/wiki/Total_variation_distance_of_probability_measures So apparently for the finite case, \max_{x} ( \left| P(x) - Q(x) \right|)\quad \mbox{ is equivalent to}\quad \frac{1}{2} \sum_x {\left| P(x)-Q(x)\right|}...

Hi, I am doing my revi[FONT="Arial"]sion and one of the question got me thinking but I am not sure if I got it right. The question asks what is the effect of variation of steam supply on power output,power factor,armature current and load angle of the synchronous machine. I think...

I was looking at section 7.6 of Longair's Galaxy Formation, and in it, he is talking about the flatness problem, or fine-tuning problem. In it, he shows that if you define a general (i.e. varies with cosmic time and hence with redshift) density parameter \Omega_m for matter by analogy with...

Homework Statement (D^2 + 2D + 1)y = ln(x)/(xe^x) Homework Equations D = d/dx The Attempt at a Solution First I find the roots of the left side of the equation, -1 of multiplicity 2. This leads to y(c) = Ae^(-x) + Bxe^(-x) Substituting A and B with a' and b' and dividing...

Given the following data for three possibile investments, A, B and C, calculate the coefficient of variation and with the aid of a diagram explain which is the least risky investment. Expected Profit: A - 100 B - 120 C - 140 Standard Devi.: A - 10 B - 30 C - 20 I presume to calculate the...

Given the following data for three possibile investments, A, B and C, calculate the coefficient of variation and with the aid of a diagram explain which is the least risky investment. Expected Profit: A - 100 B - 120 C - 140 Standard Devi.: A - 10 B - 30 C - 20 I presume to calculate the...

I am trying to solve the following equation using the variation of parameters method d2x/dt2-(q2Bz2/m2)x=qEx/m I have put x1=cos(t) and x2=sin(t) into the Wronskian method. Can someone tell me if these are the correct functions to use, or should I be using exponential functions. Any...

! Cyclic variation of engine torque If the cylinders fire sequentially according to the fire order 1-2-4-3 What is the pattern of the cyclic variation of each cyclinder engine torque and the resultant engine torque?

Hi all, I m not a physicist but a biological oceanographer. I would like to know how should I consider space-time variations of tiny cells in the ocean? Usually people deal with space and time separately but do not compute the data over a space-time scale (which I believe is important...

Homework Statement In discharge mode, calculate the variation in mass of the compounds of a lead-acid battery if the sufuric acid mass decreases by 294g (3 moles). Homework Equations The semirreactions: Pb \to P{b^{2 + }} + 2{e^ - } 4{H^ + } + Pb{O_2} + 2{e^ - } \to P{b^{2 + }} +...