Variation Definition and 540 Threads

I have come across a MATLAB code for solving the spruce budworm differential equation.But,I would like to solve the same differential equation for a range of parameters(r=0:5,q=0:10).I am having problems trying to define the array of matrices for each loop.Please look at the code below:% This...

Homework Statement This is not homework but more like self-study - thought I'd post it here anyway. I'm taking the variation of the determinant of the metric tensor: \delta(det[g\mu\nu]). Homework Equations The answer is \delta(det[g\mu\nu]) =det[g\mu\nu] g\mu\nu...

I am considering the variation of \delta ( \sqrt{g} R_{abcd} R^{abcd} ) and I know the answer is - \frac12 \sqrt{g} g_{\mu\nu}R_{abcd} R^{abcd} +\sqrt{g} R_{( \mu}{}^{bcd} R_{\nu ) bcd} + \ldots what i do not understand is the coefficient of the last term. For example, when we...

The ODE to solve via variation of parameters is ##(1-x)y''+xy'-y=(1-x)^2##. Knowing that ##e^x## and ##x## are solutions to the homogeneous ODE. Now if I call ##y_1=x## and ##y_2=e^x##, the Wronskian is ##W(y_1,y_2)=e^{x}(x-1)##. According to...

Homework Statement I must solve ##y''+2y'+2y=e^{-t}\sin t##. I know variation of parameters might not be the fastest/better way to solve this problem but I wanted to practice it as I never, ever, could solve a DE with it. (Still can't with this one). Though the method is supposed to work...

Homework Statement At time t < 0 there is an infinite potential for x<0 and for x>0 the potential is 1/2m*w^2*x^2 (harmonic oscillator potential. Then at time t = 0 the potential is 1/2*m*w^2*x^2 for all x. The particle is in the ground state. Assume t = 0+ = 0- a) what is the probability that...

Homework Statement the spring of the pressure gauge. has a force constant of 1250 N/m, and the piston has a diameter of .012m. As the gauge is lowered into water in a lake, what change in depth causes the piston to move by .0075 m Homework Equations P= P_{0} + \rhogh variation with...

x²y"(x)-3xy'(x)+3y(x)=2(x^4)(e^x) =>y"(x)-(3/x)y'(x)+(3/x²)y(x)=2x²e^x i don't know how to approach this problem because the coefficients are not constant and i am used to being given y1 and y2 HELP!

1a. Homework Statement Hi all, I'm having quite a bit of problem on a physics question. I've seen some examples of this problem, but when I follow the suggestions and equations out, the answer I get back is wrong... Anyways, here's the problem: Given two masses (m_1,~m_2) hanging from...

Here's the proof that I read for method of variation of parameters- https://www.physicsforums.com/attachment.php?attachmentid=52267&stc=1&d=1351081780 What I couldn't understand is that how could one simply assume that u'1y1+u2'y2=0 and u'1y'1+u2'y'2=g(x) I just don't understand...

I was recently trying to prove the variation of parameters formula for an nth degree equation, and I have come up with a question about the assumptions made during the derivation. During the derivation we assume that: u1'y1(k) + u2'y2(k) + . . . + un'yn(k) = 0 for k < n-1. It leads to the...

Homework Statement One body of constant pressure heat capacity C_P at temperature T_i it's placed in contact with a thermal reservoir at a higher temperature Tf. Pressure is kept constant until the body achieves equilibrium with the reservoir. a) Show that the variation in the entropy of the...

I am familiar with basic calculus of variations. For example, how to find a function that makes some integral functional stationary (Euler-Lagrange Equations). Or for example, how to perform that same problem but with some additional holonomic constraint or with some integral constraint. The...

I have a very limited knowledge of tensor calculus, and I've never had proper exposure to general relativity, but I hope that the people reading this forum are able to help out. So I'm doing some stat. mech. and a part of a system's free energy is \mathcal{F} = \int V(\rho)\nabla^2\rho dx I'd...

Homework Statement Folks, how is the following expansion obtained for the following function ##F(x,u,u')## where x is the independent variable. The change ##\epsilon v## in ##u## where ##\epsilon## is a constant and ##v## is a function is called the variation of ##u## and denoted by...

I have the equation x + y = z. Z is a constant. What type of variation is expressed here? An example of direct variation is x*z = y. An example of inverse variation of x * y = z. In both examples, z is a constant. So what's the answer?

Question: Find the total kinetic energy per unit volume in a monoatomic gas at standard temperature and pressure and deduce an expression for the variation of this kinetic energy with temperature if the pressure is maintained constant. [Standard pressure = 1.01E5 Pa] Attempt: Pressure...

Homework Statement y''-2y'+y = \frac{e^x}{1+x^2} Homework Equations u_1 = -\int \frac{y_{2}g(x)}{W}dx u_2 = \int \frac{y_{1}g(x)}{W}dx g(x) = \frac{e^x}{1+x^2} W is the wronskian of y1 and y2. The Attempt at a Solution The characteristic equation for the homogenous solution...

Is it possible to take the variation of the Dirac delta function, by that I mean take the functional derivative of the Dirac delta function?

Homework Statement solve the following differential equation: t4x'' - 4t3t' + 6t2x = - 12t - 20 Homework Equations substitution x(t) = tn The Attempt at a Solution this is a Euler equation with the following general solution: x(t) = c1t2 + c2t3 worked out using the above substitution. The...

The variation method for approximating the the ground state eigenvalue, when applied to higher energy states requires that the trial function be orthogonal to the lower energy eigenfunctions.In that respect this book I am referring(by Leonard Schiff) mentions the following function as the...

This is very simple question, and i just need a 2nd opinion. We have a Space Station (preferably a torus) with angular velocity ω and radius r. We have a car inside which OPPOSES the angular velocity and moves with the speed ωr . So, will the gravity felt in this car be Zero? Or will it be...

Most number theorists will be familiar with the result conjectured in the 19th century and proved in the 20th century that the only square pyramidal numbers that are square numbers are 1 and 4900 (the sum of the squares from 1^2 to 24^2 = 70^2). While discussing this, it was pointed out to me...

Homework Statement y'' + y' = 4t Homework Equations Use Variation of parameters! The Attempt at a Solution So I get homo of: c1 + c2 e^-(t) From there I get a Wronskian of -e^(-t) Then I get variations 2t^2 and -4e^t(t-1) Then get the answer of 2t^2 + 4t - 4 Btu...

Hi folks, In a followup to another thread about the recent controversial results by Webb et al. suggesting that the fine structure constant (alpha) varies across the visible universe, I was wondering: Assuming the Webb et al. results are correct (a big assumption), would we be able to say...

Hey, The question is displayed in the image below: So I have approached this question using g=-GM/(r^2), for the surface and the Earth as a whole. Though when it talks about the average density I wasn't sure if it meant the whole Earth or a sphere at a smaller radius (that of the...

Hey guys. In my mechanics course, we have began discussing calculus of variations, and I don't really understand what's going on, entirely. Any help understanding would be great. Our professor gave us an easy problem, but I feel like I am just missing something. Homework Statement...

NOTE : My Current question and source of debate is in post number 10. Lets say I have a square coil. I accelerate it in a direction such that it is perpendicular to a magnetic field directed into the page. As it enters the field and before it is completely in the field an...

This question about the variation of the aforementioned quantities in a transformer. Now according to me and my knowledge of electricity this is how I feel it should play out : If the input current were a sine curve that varies with time then : Input voltage = cosine curve i.e. it is...

Hi, I've come across a question in a stats book which asks the following: Q: A study was undertaken to find the relationship between "emotional stability" and performance in college. The following results were obtained: Emotional stability, Mean = 49, Standard Dev = 12 College Average, Mean...

Homework Statement Original Monty Hall problem: There are 3 doors, 1 of them contains a car and the other 2 goats. You choose 1 door, the host opens a door that is not chosen by you and does not contain the car. Then you can change to the other closed door, or keep your own chosen door at...

Hi, I'm not exactly sure how to solve the following non-homogeneous ODE by variation of parameters. Solve the given non-homogeneous ODE by the variation of parameters: x^2y" + xy' -1/4y = 3/x + 3x Can someone please point me in the right direction? Help will be much appreciated...

Hello new to this forum , Was solving some Diff eq problems and iam getting two different answers using two methods, ok the problem is i=primes (x^2)(y^ii)+(x)(y^i)+y=4sin(lnx) This is cauchy method, When i use variation of parameters i get a long answer with impossible integrals and when i...

Homework Statement Solve y''+25y=10sec(5t) Homework Equations NA The Attempt at a Solution I believe I have the correct answer for yp which is: 2/5log(cos(5t))cos(5t)+2tsin(5t) When I plug this into the Webwork field, it says it is incorrect. I checked my answer against...

Hey ya'll! This is the equation under discussion: y'' - 2y' - 3y = x + 2 I'm asked to use the method of variation of parameters to determine a solution for this differential equation, but I reach a point where my the equations just look too ridiculous to continue. The point I have in...

i m little confusd in (finding the shortest distance b/w two points is a straight line in three dimensions)i have solved it but nothing found any accurate result [ds][/2]=[dx][/2]+[dy][/2]+[dz][/2] is the distance in 3-dimension b/w 2 points then how we can start and how we can take...

Homework Statement what is general solution of 2y'' - 3y' + y = ((t^2) + 1)e^tHomework Equations my particular solution is: (e^t) ((2/3)(t^3) + 6t -4)) prof particular solution is: ((1/3)(t^3)(e^t)) - 2(t^3)(e^t) + 9(te^t) The Attempt at a Solution here is how i solved , i hope this is ok to...

Total variation is defined by \Delta f=\delta f+\Delta x For example f(x,y)=yx, y=y(x) \Delta f=x\delta y+\Delta x How is defined \Delta x. Is that rate of change of x, while y is constant?

As you will see this is my first post so I apologize if I have chosen the wrong sub-forum. My academic training (maths) was many years ago and it now seems to me that for the last 30 or so years my brain has been in a kind of intellectual limbo from which it is only now beginning to emerge, so...

Homework Statement Given, β=100, Is = 6E-16 See attachment. a) Find min value of Rb such that the BJT is in active region b) For the Rb found, what is the base-collector voltage if β=200 Homework Equations The Attempt at a Solution Assuming, VCE min for active region operation...

Homework Statement A sample of 1.00 mol of an ideal diatomic gas, initially at pressure P and volume V, expands until it has a pressure of 2P and a volume of 2V. What's the entropy change in the gas on this process? Homework Equations 2nd Maxwell relation: 4th Maxwell relation...

If f has minimum, than \delta f=0, \delta^2 f>0 or \delta f>0?

Homework Statement The goal of the question I'm being asked is to show that the covariant derivatives, D_{\mu}, "integrate by parts" in the same manner that the ordinary partial derivatives, \partial_{\mu} do. More precisely, the covariant derivatives act on the complex scalar field...

Hi all, I'm reading Sean Carroll's Space Time and Geometry and haven't figure out how equation 4.64 is derived, where he is in the process of deriving Einstein's equation from Hilbert action. Given there is a variation of the metric, g_{\mu\nu} \rightarrow g_{\mu\nu} + \delta g_{\mu\nu}, The...

If in the twin paradox instead of the twin traveling to the distant star let's say he stays and the Earth along with that star moves (imagining a rod joining Earth and star moves) and the star reaching this twin goes back at the same speed(along with earth) now i guess the twin whos stationary...

I'm not sure if this is the right place to post this, but it seems to be the best fit. Homework Statement I'm trying to write a lab report about how resistance varies with temperature. I used liquid nitrogen to cool a copper coil and a semiconductor(thermistor) from room temperature to...

Frequency distribution not determined by the temporal variation of the pulse? In his book Modern Optical Spectroscopy, William Parson says Light from an incoherent source such as a xenon flash lamp contains a distribution of frequencies that are unrelated to the length of the pulse...

Hi, In the usual Gambler's ruin problem one calculates the probability of reaching some target balance N before going broke, given that one starts with holdings of 'h', and given that on each bet he either increases or decreases his balance by +/-1. See...

Homework Statement By what factor is the total pressure greater at a depth of 850 m of sea water than at the surface where the pressure is one atmosphere? (water density = 1000 kg/m3, one atmosphere pressure = 1.01 x 105 Pascals (N/m2), g = 9.8 m/s2 ) Homework Equations P=P(initial)+ρgh...

Problem - Given the following table x y 15 50 26 46 32 44 48 43 57 40 a) Find the sample mean b) Find the covarince matrix c) Perform principal component analysis and find a size index which explains the greatest variation. My attempt a) n = 5 xbar = Sum(x)/n = 35.6 ybar =...