Partial Definition and 1000 Threads

One last question to Integrate x^2/(1+4•x^2). I would assume you would do long division but 4x^2 is bigger than x^2. so would you either pull out a 1/4 and it would be 1/4 ∫ x^2/(1/4+•x^2) dx or would the first term when doing long division be 1/4? or am I just totally wrong and you...

the probability of finding particle is a constant with time <ψ|\partialψ/\partial(t)> = -<\partialψ/\partial(t)|ψ> , the equation holds for all ψ so the time derivative operator is an anti-hermitian operator, but then consider any hermitian operator A, the rate of change of A is d(<ψ|Aψ>)/dt =...

Ok all save y'all a little reading. Worked out the problem. Got X^2+2x-1=A(2x-1)(x+2)+bx(x+2)+cx(2x-1) Ok then you write it standard form for a polynomial. Then use can use there coefficients to write new equations at you get 2a+b+c=1 3a+2b-c=2 and finally -2a=1 Now you solve for...

$x = r\cos\theta$ and $y=r\sin\theta$ $$ \frac{\partial u}{\partial\theta} = \frac{\partial u}{\partial x}\frac{\partial x}{\partial\theta} + \frac{\partial u}{\partial y}\frac{\partial y}{\partial\theta} = -r\sin\theta\frac{\partial u}{\partial x} + r\cos\theta\frac{\partial u}{\partial y} $$...

Homework Statement Consider an object that is coasting horizontally subject to a drag force f = -bv = cv^2. Write down Newton's second law... The Attempt at a Solution So I did all of the steps leading up to this: m∫\frac{dv}{bv+cv^2}=-t dt Using partial fractions I get \frac{1}{bv+cv} =...

Any help would be much appreciated - Is it possible to say the following? If z = g(s+at) + f(s-at), let u = s+at and v=s-at, where a is a constant. z = g(u) + f(v), \frac{∂z}{∂u} = g'(u), \frac{∂^{2}z}{∂v∂u} = 0? or can ∂u and ∂v not even exist because it depends on two variables (a and...

Use a geometric or algebraic argument to find a formula for the partial sums $A_n$ of an arithmetic sequence. I know that the partial sum is $S_n = n/2(2a_1+(n-1)d)$ where d is the difference. $A_n = \sum\limits_{k = 1}^n a_k$ I can come up with $n/2(a_1+a_n)$ but how do I get the difference?

Hi I am currently looking at some literature for the production of different radioactive nuclei under the bombardment of protons on Copper. I found something called partial γ-ray production cross-sections and I am wondering what this means. I know that cross-sections generally describe the...

I am working on some problems for an assignment in my PDEs class and find myself either not understanding what I am supposed to do or being unsure of my answers or the next step. I am going to outline my understanding of the problems, provide my attempt at a solution and highlight where I am...

Homework Statement ∇^{2}u=0 on 0<x<∏, 0<y<2∏ subject to u(0,y)=u(∏,y)=0 and u(x,0)=0, u(x,2∏)=1Homework Equations -- The Attempt at a Solution I've solved the SLP, and now I am trying to solve the Y-equation that results from separation of variables: Y''-λY=0, Y(0)=0...

Homework Statement determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx Homework Equations partial fractions technique The Attempt at a Solution i know it's partial fractions and i thought i did it right but i got the wrong answer. (4x+10)/(9x^2+24x+16) =...

Homework Statement Prove that (∂P/∂V) n,T = 1/(∂V/∂P) n,T n and T are supposed to mean that theyre just constants Homework Equations Ideal Gas PV=nRT The Attempt at a Solution I tried (∂P/∂V) n,T= ∂nRT/v/∂V = ∂nRT/V ∂V then I am stuck here

Homework Statement Find ∫18/((x2+9)(x-3)) Homework Equations The Attempt at a Solution Im a little stuck on this. 18∫1/((x2+9)(x-3)) Im not sure how to turn this into a partial fraction.. help. Thanks

Homework Statement Please look at the attached pic. I don't know how to type all these symbols in. Homework Equations Im not sure how to start The Attempt at a Solution I tried using the cyclic rule but the problem just started getting messier.

Homework Statement Parametrize the upper half of the unit circle by x = cos(t), y = sin(t), for 0\leq t \leq\pi Let T = f(x,y) be the temperature at the point (x,y) on the upper half of the circle. Suppose that: \frac{\partial T}{\partial x} = 4x - 2y \frac{\partial T}{\partial y} = -2x +...

For PFE, can a denominator variables with coefficient of something other than 1, or does it have to be 1? For Example, can I have a term A/(3x+9)? It's been years since I've dealt with this and don't quite remember if this was a rule or not. Thanks! EDIT: This is in terms of taking the...

Homework Statement I need to integrate v(t) = V( \frac{1- e^{-2gt/V}}{1+ e^{-2gt/V}}) to show that the position function is given by s(t) = Vt + \frac{V^2}{g}ln(\frac{1 + e^{-2gt/V}}{2}) Homework Equations g is the acceleration due to gravity V is the terminal velocity The Attempt at...

find the valu of local extremum for f(x)=sin x-cos x,0<x<2∏.

Im reading Lang's first course in calculus and can't understand one step that he does when trying to integrate quotients with quadratic factors in the denominator. He's trying to find the integral of \int{\frac{1}{(x^2+1)^n}dx} but he's first starting with the case where n=1 Then while...

say you have a function f(x,y) \nablaf= \partialf/\partialx + \partialf/\partialy however when y is a function of x the situation is more complicated first off \partialf/\partialx = \partialf/\partialx +(\partialf/\partialy) (\partialy/\partialx) ( i wrote partial of y to x in case y was...

Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...

hello, I've spent a good couple hours diving back into the world of differential equations after being out of the game for a good 2 years. I started getting a hang of solving them till i came across this problem: Solve the following differential equation with the 3 given cases, all of the...

Find the first order partial derivatives of the function x = f(x,y) at the point (4,3) where: f(x,y)=ln|(x+√(x^2+y^2))/(x-√(x^2+y^2))| I understand the method of partial derivatives and implementing the given point values once the partial derivatives are found, however I am having trouble...

Homework Statement The problem is attached in the picture. The Attempt at a Solution I'm aware that: dU = T dS - P dV ∫ dU = ∫ (T) dS - ∫ P dV Are they assuming that T, P are constant so U = TS - PV ∂U/∂X = T (∂S/∂X) - P (∂V/∂X) Or is there a way to directly...

Partial Pressure Help---Please Check The Partial Pressure of water vapor at T = 273 K is 6.11 mbar. Find the corresponding mass concentration of water vapor. Assume P = 1 atm. So... ρH20 = (PH20*MH20/(R*T) ρH20= (6.11*10^2 Pa)*(18.01 g/mol)/(8.314*273 K) ρH20 = 11004.11/2269.722 =...

Folks, I am stuck on an example which is partial differenting a functional with indicial notation The functional ##\displaystyle I(c_1,c_2,...c_N)=\frac{1}{2} \int_0^1 \left [ \left (\sum\limits_{j=1}^N c_j \frac{d \phi_j}{dx}\right )^2-\left(\sum\limits_{j=1}^N c_j \phi_j\right)^2+2x^2...

hello world, I've been doing some summertime training to brush up my math skills and have been struggling with this [dy]/[/dt]=(4exp(-y)+const*exp(-2y))^1/2 In fact this is the simplified version of a Bernouilli equation. I know that it is separable, I'm just struggling with the...

Homework Statement Use partial fractions to find the sum of the series: \Sigman=1 to infinity \frac{5}{n(n+1)(n+2} Homework Equations Partial Fraction breakdown: \Sigma \frac{5}{2n}+\frac{5}{2(n+2)}+\frac{5}{(n+1)} The Attempt at a Solution When I tried to cancel terms out, it is...

I have been having trouble of late with partial fraction decomposition. Not so much the maths, but the intuition behind it. What I mean by this, but a question in front of me, I now what procedure to follow to get the answer, but I don't get why you follow the said produced. I will give an...

A 3-dimensional graph has infinite number of derivatives (in different directions) at a single point. I've learned how to find the partial derivative with respect to x and y, simply taking y and x to be constant respectively. But what do I do if I want to take the partial derivative with respect...

Hi! Here is my function: My task is to find: I think I know how to find ∂u/∂x, but I have no idea how to find ∂/∂z(∂u/∂x). Here is how I found ∂u/∂x: http://oi48.tinypic.com/prsly.jpg Does someone know how to find ∂/∂z(∂u/∂x)? I appreciate any help :)

Hi all, I have the following partial derivatives ∂f/∂x = cos(x)sin(x)-xy2 ∂f/∂y = y - yx2 I need to find the original function, f(x,y). I know that df = (∂f/∂x)dx + (∂f/∂y)dy and hence f(x,y) = ∫∂f/∂x dx + g(y) = -1/2(x2y2+cos2(x)) + g(y) Then to find g(y) I took the...

Hello, In my study i came across to solve the analytical solution for coupled equation y(x,t) and z(x,t).The equations contains" f " function which is a function of the first variable exponentially. The first equation is : ∂y/∂t=∂^2(y)/∂x^2- 2*f(y)*z; The second equation ...

Homework Statement The problem is attached in the picture. The top part shows what is written in the book, but I am not sure how they got to (∂I/∂v)...The Attempt at a Solution It's pretty obvious in the final term that the integral is with respect to 't' while the differential is with...

Homework Statement This question is about entropy of magnetic salts. I got up to the point of finding H1, the final applied field. The Attempt at a Solution But instead of doing integration I used this: dS = (∂S/∂H)*dH = (M0/4α)(ln 4)2 I removed the negative...

Hi, I'm reading about the partial wave expansion in Shankar. In his method, we expand the incident plane wave (he chooses it such that it's coming in along the z axis, and using spherical coordinates) using the Legendre polynomials: e^{ikr cos(\theta)} = \sum _{l = 0} ^\infty i^l (2l + 1)...

Homework Statement The equations xu^2 + yv = 2, 2yv^2 + xu = 3 define u(x,y) and v(x,y) in terms of x and y near the point (x,y) = (1,1) and (u,v) = (1,1). Compute the following partial derivatives: (A) ∂u/∂x(1,1) (B) ∂u/∂y(1,1) (C) ∂v/∂x(1,1) (D) ∂v/∂y(1,1) The answers are: (A)...

I am unsure how to (mathematically) do the partial trace of a density matrix so that I can find the expectation value of an observable. I am working on a model similar to the Jaynes cummings model. My density matrix is of the form; \rho = [\rho_{11}, \rho_{12}, \rho_{21}, \rho_{22}]...

Hello every one, In my physics problem, i end up having two coupled second-order nonlinear differential equations where the coupling terms include, the variable, the first derivatives, and also a second derivative coupling. I appreciate any help on how to handle this system before setting it...

Homework Statement find dz/dy(partial) z= tan-1(y/x) Homework Equations The Attempt at a Solution z= tan-1(y/x)let u=y/x z= tan-1(u) dz/du = 1/ (1+u2) so dz/dy = dz/du (du/dy) du/dy = 1/x so dz/dy = (1/1+u2)(1/x) = 1/ 1+ (y2/x2) * 1/x = 1/ x + (y2/x2)x) = x / x + y2but I should be...

Homework Statement 1. Is (∂P/∂x)(∂x/∂P) = 1? I realized that's not true, but I'm not sure why.2. Say we have an equation PV = T*exp(VT) The question wanted to find (∂P/∂V), (∂V/∂T) and (∂T/∂P) and show that product of all 3 = -1.The Attempt at a SolutionI tried moving the variables about...

Homework Statement The changing variable formula in partial derivative f(u,v) x=x(u,v) y=y(u,v) (∂f/∂x)y = (∂f/∂u)v(∂u/∂x)y + (∂f/∂v)u(∂v/∂x)y I khow the how chain rule works, but I don't know why in the (∂f/∂u) v is constant and in the (∂u/∂x) y is constant Homework Equations The...

I just got to a point in multivariable calculus where I realize I can solve problems in assignments and tests but have no actual idea of what I'm doing. So I started thinking about stuff and came up with a few questions: 1. Is picturing the derivative as the slope of the tangent line to a...

Homework Statement In the first paragraph, I know its missing a function which they did not put, g. Without puting ∂g/∂x but simply putting ∂/∂x, is that equation even mathematically correct? I know they are "filling in the g later" but does this corrupt the in-between steps in anyway? In the...

Yo guys,I was wondering if there was an easy logical way of finding a general n-th term in a sequence of partial sums for any converging sequence {a-n}

I have calculated 3 times and I still don't get the answer. The answer should be 0. Here's the question and my work. Which part am I wrong?f(x,y) = 1/√(1-2xy+y^2) Prove that ∂/∂x{(1-x^2)*∂f/∂x} + ∂/∂y{(y^2)*∂f/∂y} = 0

I have calculated 3 times and I still don't get the answer. The answer should be 0. Here's the question and my work. Which part am I wrong? f(x,y) = 1/√(1-2xy+y^2) Prove that ∂/∂x{(1-x^2)*∂f/∂x} + ∂/∂y{(y^2)*∂f/∂y} = 0

Homework Statement Hey, i ve got problem with a few partial derivative problems. 1.I have a function T(x,t) Prove that dT/dt=∂T/∂t +∂T/∂x dx/dt 2.Let u(x,y) and y(x,u) be continous, differentiable functions. Prove that ∂u/∂z=∂u/∂z ∂y/∂z 3 Let r(q1,q2,...qn) be a function of place...

Homework Statement What does it mean when lowercase Delta (δ) is used in partial derivative and derivative notation? Does it make any difference? Or is it just a personal preference? Homework Equations - The Attempt at a Solution Google

I want to understand how to compute (or find a database for) partial charges, which I can then apply to calculating coulombic interactions. From http://www.chemaxon.com/marvin/help/calculations/charge.html, it is said that electronegativity is related to the partial charge by a quadratic...