Partial Definition and 1000 Threads

Hi, I'm working on a modified version of the Jayne's Cummings model and am a little confussed. I have: -Taken modified version of JCM Hamiltonian in Schrodinger picture. -Used Von Neumann equation to get evolution of density matrix -Converted to Wigner function. I want to run...

We have a function f:R^2->R and it has partial derivative of 2nd order. Show that f_{xy}=0 \forall (x,y)\in \mathbb{R}^2 \Leftrightarrow f(x,y)=g(x)+h(y) The <= is self explanatory, the => I am not sure I got the right reasoning. I mean we know that from the above we have: f_x=F(x) (it's...

Homework Statement \frac{2e^3}{((s^2)-6s+9)*s^3} you can factorize the denominator into s,s,s,(s-3),(s-3) that gives you 5 residuals. the first 3 should all be the same value but that's apparently not correct, so where am I going wrong?

Homework Statement given z=yf(x^2-y^2) show that the x(∂z/∂y)+y(∂z/∂x)=xz/y The Attempt at a Solution cut it short, my ∂z/∂y= f(x^2-y^2)-2(y^2)f(x^2-y^2) ∂z/∂x=2xyf(x^2-y^2) i was able to prove that x(∂z/∂y)+y(∂z/∂x)=xz/y But i need help with partial differentiations...

Homework Statement I'm supposed to decompose 1 / x(x2 + 1)2 Also, we haven't learned matrices yet so I can't use that technique to solve it. Homework Equations None. The Attempt at a Solution 1 / x(x2 + 1)2 = A/x + (Bx + C) / (x2 + 1) + (Dx + E) / (x2 + 1)2 I multiplied...

Homework Statement Find a closed form for the nth partial sum, and determine whether the series converges by calculating the limit of the nth partial sum. 1. 2+2/5 + 2/25+...2/5k-1 Homework Equations The Attempt at a Solution What I did was I found out it was a geometric...

Homework Statement Find the partial derivatives: f(x,y)= integral[x,y] cos(t^2)dt, find f_x(x,y) and f_y(x,y) Homework Equations I know from calculus that the derivative of an integral is the function. The Attempt at a Solution I found that the integral of [x to y]...

Homework Statement The electric potential in a certain region of space is given by: V(x,y,z) = 1000x-2000y-1500z(Volts). a.)Find the electric field corresponding to the given electric potential. Draw some electric field lines. b.) What charge distribution can create this electric field? Give...

urgent reply needed Can we use partial means as a predictor for the response while fitting a regression line or curve?.

Homework Statement Inverse Fourier of: [ jω+2 ] / [ (jω)2 +5jω+9 ] where j = sqrt(-1) I tried using partial fractions but the denominator can't be factored...I tried completing the square on the denominator but I get a sum of squares. What can I try? I am sure I don't have to use the formal...

Homework Statement ∫(x3+4)/(x2+4)dx Homework Equations n/a The Attempt at a Solution I know I have to do long division before I can break this one up into partial fractions. So I x3+4 by x2+4 and got x with a remainder of -4x+4 to be written as x+(4-4x/x2+4). Then I rewrote...

Homework Statement The question is attached along with its solution. Homework Equations Partial differentiation and the implicit function theorem. The Attempt at a Solution My work is attached. I feel it's correct but is it incomplete? I have the following questions/confusions...

When you have waves that are out of phase by some fraction of a cycle, e.g not exactly in phase and not exactly 180 degrees anti-phase, how do you determine the phase (relative to the original component waveforms) of the resultant? Specifically, is there an equation that solves for phase...

Hello Experts I have a simple question. Given V as the function of Z and Y, Given Z as the function of R and L, Z=R+s*L Given Y as the function of G and C, Y=G+s*C Assume we also know \frac{\partial V}{\partial Z} and \frac{\partial^2 V}{\partial Z \partial Y} If we want to know...

Hi, I find my professor doing this a lot of times, here is it: ∫{ ∂(f[x])/∂x } dx = ∫d(f[x]) How is that possible?

Homework Statement Given 4 state variables x, y, z and w such that F(x,y,z)=0 and w depends on 2 of the other variables, show the following relations: 1)\left ( \frac{\partial x }{\partial y } \right ) _z = \frac{1}{\left ( \frac{\partial y }{\partial x } \right ) _z} 2)\left (...

Can this be done? If so, how can I go about doing so? This is merely a potential science fair idea for 2013.

Homework Statement We were given a worksheet to integrate some problems using partial fractions. This one however I cannot figure out what to do with it. This is the problem. ∫(x3-4x2+x+6)/(x2-x+2) dx The Attempt at a Solution using long division i got ∫(x-3) (-4(x-3)/(x2-x+2) dx...

I wanted to compute the conditional pearson correlation (CPC). First, I wanted to make sure if it is OK to use the absolute pearson correlations in the computation of CPC. Becuase I think only the strength of pairwise correlations should be considered in computing CPC, and not the sign. Second...

Homework Statement w = 2xy + 4yz + 5xz x = st y = 3^(st) z = t^2 s=5 t=1 Homework Equations Chain rule: xy = x*y' + y*x' The Attempt at a Solution w = 2stest + 4test + 5st3 (partial derivatives) dw/dt = 2s2test + 2sest + 4tsst + 4est + 15st2 (partial derivatives) dw/dt (5,1) = 2(5)2e5 +...

$$ \frac{1}{z^2(1-z)} = \frac{A}{z^2}+\frac{B}{1-z} $$I can't figure out how to decompose this fraction.

Homework Statement In the steps below, the ∂z/∂x does not seem to be obeying normal algebraic rules. I'm confused. This is not really a problem, I'm just trying to understand the steps. The Attempt at a Solution 1. 3z2∂z/∂x - y + y∂z/∂x = 0 2. ∂z/∂x = y/(y + 3z2) if ∂z/∂x were...

If you have a function f(x,y)=xy where y is a function of x, say y=x^2 then the partial derivative of f with respect to x is \frac{\partial f}{\partial x}=y However, if you substitute in y and express f as f(x)=x^3 then the partial derivative is \frac{\partial...

Homework Statement The question is attached as Question.jpg. Homework Equations Partial differentiation. The Attempt at a Solution This seems obvious to me but I don't know how to express myself mathematically. Basically, what I'd do is: [∂(u,v)/∂(x,y)] [∂(x,y)/∂(r,s)] =...

Homework Statement ∂f/∂x (xy -1)2 = 2y(xy-1) The Attempt at a Solution I would think the answer would be 2(xy-1) I don't understand where the y comes from in 2y

Homework Statement If f is a quadratic function such that f(0) = 1 and \int \frac{f(x)}{x^2(x+1)^3}dx is a rational function, find the value of f '(0). Homework Equations The Attempt at a Solution This question is presented in the context of learning about integration by...

Homework Statement I don't understand why ∂f/∂x = xy = y whereas ∂f/∂x = x2 + y2 = 2x Why does the y disappear in the second but not in the first?

So I don't understand why if you have something like U(x,y) = f(y+2x) and you take \frac{\partial U}{\partial x} = \frac{\partial f}{\partial x} you get \frac{df}{d(y+2x)} * \frac{d(y+2x)}{dx} Why does the partial derivative just change to the total derivative for one variable? It...

Homework Statement I can't seem to find information on this specific question i have. So I'm taking the partial derivative of this equation for both x and y I know how to do it for y, but I am not seeing something with respect to x fx(x,y)= x^7 + 2^y + x^y Homework Equations The Attempt at...

Hi everyone: How is the following derived? Just for example: \Deltax\alphae\alpha=\Deltax\alpha(\delta/\deltax\alpha) does it not mean? e\alpha=\delta/\deltax\alpha But How?

Have worked through to get some sort of answer, but find the evaluation (simplest bit) impossible - wood for trees, I think. given d2(e^(xy^2)/dy^2 I need to evaluate for x=2, y=0 now using chain rule d(e^(xy^2))/dy = d(e^u)/du du/dy where u=xy^2 & d(e^u)/du = e^u => x(2y) e^(xy^2) fine...

Homework Statement This is the first problem of the two. Homework Equations The Attempt at a Solution Using separation of variables, I end up with T'(t)= -λKT(t) and X''(x)+(β/K)X'(x)/X(x)= -λ. At first I chose the negative lambda because I saw that U(0,t) and U(L,t) needed to oscillate...

Homework Statement I have the series 1^3+2^3+3^3...n^3, and need to find a formula containing n to represent the sum of the nth terms. The motivation is to find a conjecture, which I can then prove using mathematical induction. The Attempt at a Solution I see that n=1 , 1^3=1...

Homework Statement Suppose the function f:R^2→R has 1st order partial derivatives and that δf(x,y)/δx = δf(x,y)/δy = 0 for all (x,y) in R^2. Prove that f is constant; there exists c such that f(x,y) = c for all (x,y) in R. There's a hint as well: First show that the restriction of...

Homework Statement The solubility of N2 in blood at 37 degree and at a partial pressure of 0.8 atm is 5.6 x 10-4 mol/L? a deep sea diver breathes compressed air with the partial pressure of N2 equal to 4 atm. Assume that the total volume of blood in the body is 5 L. Calculate the amount of N2...

I am checking my homework with mathematica, but sometimes when I write stuff like D[(x/((x^2 - y^2)^0.5)), y] , which is supposed to give me the partial derivative of x/((x^2 - y^2)^0.5) with respect to y, i get answer like: (1. x y)/(x^2 - y^2)^1.5 which is right, except for the...

I was reading a section on vector fields and realized I am confused about how to take partials of vector quantities. If V(x,y)= yi -xj, I don't understand why the \partialx= y and the \partialy= -x. The problem is showing why the previous equation is not a gradient vector field (because the...

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate.) ∫(x^3 + 36)/(x^2 + 36) Homework Equations The Attempt at a Solution A little bit confused about arriving at the solution for this problem. I get stuck a little ways in. Any help would be...

Homework Statement at 1000K, Kp=1.2*10^6 and Delta H = -101.7 kJ for the reaction H2(g)+ Br2(g) <-->2HBr. A 0.952 mol quantity of Br2 is added to a 1.00L reaction vessel that contains 1.25 mol of H2 gas at 1000K . What are the partial pressures of H2 ,Br2 ,HBr and at equilibrium?Homework...

If a and b are constants, compute the expression KY'(K) + LY'(L) for Y = AK^a + BL^a Y'(K) means partial derivative with respect to K by the way. The answer in the book is KY'(K) + LY'(L) = aY I'm not sure what they did or what they're asking :/

This is throwing me through so many loops. I have the equation 1/(x^3 + xa^2). I can not for the life of me decompose this equation. I use 1(x^3 + xa^2) = A/x + (Bx + C)/(v^2+a^2) I can get A=1/a^2, but from there progress stops. All examples on the internet and books only have...

I'm attaching the question and solution. I'm talking about the first part since the second part is the same just with different variables and stuff. I get what the solution is saying but: 1) What if I computed a Jacobian, with F = x^2 + xy + y^2 - z = 0 G = 2r + s - x = 0 H = r - 2s - y...

From Mary Boas's book, chapter 4. Z = x^3 -e^xy 1- Z(x) = 3x^2 y - ye^xy make sense according to derivation rule d(e^u)/dx = e^u.u` 2-Z(y) = 3^x - xe^xy make sense too. 3-Z(y)x)) = 3x^2 - e^xy - xye^xy where e^xy came from ?? Thank you.

The problem is from an online homework assignment. I know it's probably fairly simple, but my brain isn't grasping it right now for some reason.[The Problem] We know: r(t) = <3t2 - 8t + 3, -9t2 + 2t + 7> And we are asked to find d2y/dx2.[Background Information] My understanding of d2y/dx2...

Hello, Is there any general formula for the partial fraction of the following function: \frac{1}{(ax_1+1)(ax_2+1)\cdots (ax_L+1)} I can work for L=3, but it get involved for larger L! Thanks in advance

y' = (3+y)(1-y) y(0) = 2 Attempt to solve: \frac{dy}{dx}=(3+y)(1-y) (3+y)(1-y)dy = dx \int(3+y)(1-y)dy = \int dx Partial Fractions: \frac{A}{(3+y)} + \frac{B}{(1-y)} A(1-y)+B(3+y) Let y= 1 or -3 A = 1/4 B = 1/4 \frac{1}{4}\int \frac{1}{(3+y)} dy + \frac{1}{4}\int...

Homework Statement I have attached a picture of the problem. The question is the first one. Homework Equations The Attempt at a Solution I tried subbing u and v into the right hand side of the equation. I expanded and simplified but I do not think that is the right way to go...

Homework Statement I came across a problem that I can't solve and it is ∫dx/x(x^2 + 4)^2 Homework Equations None The Attempt at a Solution So I'm pretty sure this is to be solved by partial fraction since I am on a chapter on Integration by partial fraction. so I started with...

This is another problem than I've been stuck on for a long time and I tried reading and watching videos but I only find first order partial differentiation with more than two variables or higher order partial differentiation with only two variables. (I'm not calling f a variable but I am calling...

Homework Statement im not sure the elegant way to put it, i need to integrate this somehow (ie, throw over the dt and integrate each side) but that squared is really tripping me up. is there a trick i should be using? -g(cos(x))=r(dx/dt)^2 Homework Equations The Attempt at a...