Partial Definition and 1000 Threads

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...

Deriving Probability Density Functions from Partial Differential Equations? Hiyas, I have been told that it is quite normal to get PDFs (Probability Density Functions) from PDEs (Partial Differential Equations). That in PDEs that the function can be a PDF and you can get this by solving the...

And not taking ODE's? Is this doable? I understand the basics of most concepts as I am currently self-learning from online resources and textbooks, but I decided not take the class during the summer as I'm already taking calc III. The problem is that when the year starts up again PDE's is taught...

Hi everyone, I know that if z = f(x,y) = x^2y + xy^2 then \frac{\partial z}{\partial x}=2xy+y^2 and \frac{\partial z}{\partial y}=x^2+2xy Please correct me if I am wrong. In the physics, can anyone please tell me what is the meaning of below formula? \frac{\partial V}{\partial t} Where...

Homework Statement Find a differential of second order of a function u=f(x,y) with continuous partial derivatives up to third order at least.Hint: Take a look at du as a function of the variables x, y, dx, dy: du= F(x,y,dx,dy)=u_xdx +u_ydy. Homework Equations The Attempt at a Solution I'll be...

Long story short I'm making some nanoparticles and one of the steps require me to evaporate THF(tetrahydrofluran) out of an aqueous solution containing the NP's. This needs to be done under a partial vacuum with only one intake valve(I know, it sucks but I have no other option). I'm looking more...

Homework Statement I have got a question concerning the following function: f(x,y)=\log\left(x^2+y^2\right) Partial derivatives are: \frac{\partial^2f}{\partial x^2}=\frac{y^2-x^2}{\left(x^2+y^2\right)^2} and \frac{\partial^2f}{\partial y^2}=\frac{x^2-y^2}{\left(x^2+y^2\right)^2} The...

Why in partial fractions does the power of the denominator have to be one more than that of the numerator, when splitting up the expression. Skip to 5:30. Thanks.

Hello Everyone! This has been confusing me a lot: consider a function $f(x) = x^2 + 2x + 3$. Now, $\frac{\partial f}{\partial x} = 2x + 2$. Now, someone tells me that $y = x^2$. What is $\frac{\partial f}{\partial x}$ now?

Why is partial derivative with respect to time used in the continuity equation, \frac{\partial \rho}{\partial t} = - \nabla \vec{j} If this equation is really derived from the equation, \frac{dq}{dt} = - \int\int \vec{j} \cdot d\vec{a} Then should it be a total derivative with...

Homework Statement Need to find the tangent to the curve at: e^(xy) + x^2*y - (y-x)^2 + 3 I just implicitly differentiate the expression to find the gradient and then use the points given to find the equation, right? Or does this involve partial differentiation? Homework Equations...

How do gases exist at partial pressures in a mixture. Moisture in the air is superheated steam, yet at a temperature well below atmospheric boiling point, implying that the moisture in the air is at very low pressures. How does it maintain this state?

In the ordinary least squares procedure I have obtained an expression for the sum of squared residuals, S, and then took the partial derivatives of it wrt β0 and β1. Help me to condense it into the matrix, -2X'y + 2X'Xb. ∂S/∂β0 = -2y1x11 + 2x11(β0x11 + β1x12) + ... + -2ynxn1 + 2xn1(β0xn1 +...

I am having trouble finding the rule for the (partial) derivative of an expression like y = f(X)^{g(X)} can anyone help?

Could someone please explain to me how to find the derivative of this: dy/dx = φ(x, y) Should I break up the equation to make it dy/dx = φ(x) + φ(y) and then derive the parts? I would then get d²y/dx² = ∂φ/∂x + ∂φ/∂y do I have to also multiply both terms by their respective derivatives...

Now this is a pretty straight forward question. And I just want to make sure that I am not doing anything stupid. But when doing partial fraction expansions of the type \frac{K}{s^{2}+2\zeta\omega_{n}s+\omega_{n}^{2}} Shouldnt I always be able to factor the denominator into the following...

For some non-linear 3D function, let's say I want to take the partial derivative for x where y is constant. Each point for Z will be different of course since it's non-linear. So let's say I plug in an X of 3 where Y is constant for some function and I get a slope of 5 as my answer. Is it...

Dear all, I have a confusion about partial derivatives. Say I have a function as y=f(x,t) and we know that x=g(t) 1. Does it make sense to talk about partial derivatives like \frac{\partial y}{\partial x} and \frac{\partial y}{\partial t} ? I doubt, because the definition of...

imgur.com/kBTVm Hi, I understand that work done in a conservative field when a closed loop is followed is zero. The answer to this question I am sure is B. How do I explain to my colllegue that it is not zero when he thinks that the speed is constant and there is no friction and the force...

Homework Statement Let x=ts^2 -1 and y=ln(s)-t Use the chain rule for functions of two variables to determine ∂f/∂t at (s,t)=(1,1) The Attempt at a Solution y=ln(s)-t ∂f/∂t= ∂f/∂s X ∂s/∂t -1 t=x+1/s^2 ∂t/∂s= -2(x+1)/s^3 ∂s/∂t=s^3/-2(x+1) ∴ ∂f/∂t= s^2/-2(x+1)...

Homework Statement Here is the problem: http://dl.dropbox.com/u/64325990/MATH%20253/help.PNG The Attempt at a Solution http://dl.dropbox.com/u/64325990/Photobook/Photo%202012-05-24%209%2037%2028%20PM.jpg This seems to be wrong... Since I have fx and fy which I cannot cancel out. Why...

So I have a proof and I can't follow the process, I think its because I haven't learned how to do partial derivatives or I've forgotten, anyways can someone tell me if this is a rule in calculus (∂Cv/∂V)T=0 I've gotten to [(∂/∂V)(∂U/∂T)V]T and the proof I have goes to...

Directional and partial derivatives help please! I have read that the partial derivative of a function z=f(x,y) :∂z/∂x, ∂z/∂y at the point (xo,yo,zo)are just the tangent lines at (xo,yo,zo) along the planes y=yo and x=xo. Directional derivatives were explained to be derivatives at a particular...

Homework Statement ∫10x-2x2/((x-1)2(x+3)) Solve by partial fractions. The Attempt at a Solution ∫A/(x-1) +B/(x-1)2 + C(x+3) after setting up the partial fractions and multiplying each term by LCD: 10x-2x2= A(x-1)(x+3) + B(x+3) + C(x-1)2 10x-2x2= A(x2+2x-3) +Bx+3B +Cx-C 10x-2x2=...

Homework Statement If f(x,y) = x(x^2+y^2)^(-3/2)*e^(sin(x^2y)) find the derivative of f with respect to x at the point (1,0). The Attempt at a Solution The textbook solution just plugs 0 into y and gets f(x) = x^-2 and then proceeds to differentiate this resulting in the answer -2. I...

Hi, Can somebody help me solve the following PDE? ∂p(x,t)/∂t = -p(x,t) + ∫λ(x-x')p(x',t)dx' with p(x,0)=δ(x) Thanks a lot

I'm brushing up on differentiating multi-variable functions subject to a constraint and was curious about the notation. In particular, why the derivatives change from complete to partial derivates. I've illustrated the question with an example, below. My specific question w.r.t. the example is...

Now yesterday I got help in realizing how to evaluate the sums of certain series, but while doing it I never got the reason behind why we take a series such as: \sum from k=1 to ∞ 1/k(k+3), I know how to solve the sum, but why do we have to convert it to a set of partial fractions in order to do it?