Partial Definition and 1000 Threads

Is it possible to find a non-recursive formula for the partial sums of a convergent series?

I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by: dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant) v(t = 0) = C (constant value) v(x = 0) = 0 I'm not quite sure how to solve this. I was thinking about using the method of...

when we fill a container with water so as to leave some space above the surface of water. And we close the container. When we turn the tube upside down. The air which which was above the surface of water transfers to the other side. How does this happen. Does air penetrate water? And suppose...

Homework Statement So using standard spherical polar co-ordinates, my notes define a sphere as r(s,t) = aCos(s)Sin(t) i + aSin(s)Sin(t) j + aCos(t) k and the normal to the surface is given by the cross product of the two partial differentials: \partialr/\partials X \partialr/dt...

Homework Statement The activity coefficient of zinc in liquid brass is given (in joules) by the following equation for temperatures 1000-1500 K: RT ln γZn = -38,300 x2Cu where xCu is the mole fraction of copper. Calculate the partial pressure of pure zinc PZn over a solution of 60 mol%...

Homework Statement Are these two relations reflexive, antisymmetric, transitive? 1. (w,x)<=(y,z) iff w+x <= y+z 2. (w,x)<=(y,z) iff w+x <= y+z AND w<y Homework Equations The Attempt at a Solution 1. reflexive - yes; antisymmetric - no; transitive - yes; 2. reflexive -...

Homework Statement Find (x,y) which maximizes f(x,y) for x ≥ 0. f(x,y) = e-x - e-2x + (1 - e-x)(4/5 - (3/4 - y)2)Homework Equations The Attempt at a Solution Due to the question prior to this one, I know all the first order and second order partial derivatives of the formula. I do not...

Homework Statement When two resistors R1 and R2 are connected in parallel, their effective resistance R = (R1R2)/(R1+R2). Show that is R1 and R2 are both increased by a small percentage c, then the percentage increase of R is also c. Homework Equations The Attempt at a Solution I...

Homework Statement Use partial fractions to rewrite: (2z)/(z^2+3) Homework Equations noneThe Attempt at a Solution I did this: (2z)/(z^2+3) = (Az+B)/(z^2+3) 2z = Az +B A = 2, B = 0...problem is that it just recreates the original Here is their example in the book: 1/(z^2+1) =...

a) Determine K at 298K for the reaction H2(g) + Cl2(g) <---> 2HCl(g) b) The equilibrium partial pressure of HCl is 1 bar. Determine the equilibrium partial pressures of H2 and Cl2. This question was on my test. I got K= 3.2 x 10^-34 using dG*=-RTlnK when dG=0 at equilibrium. I'm having...

Homework Statement How does ∂aAb behave under coordinate transformations in special relativity? Work out ∂'aA'b Homework Equations The Attempt at a Solution I have been given back the solution sheet to this problem, but I don't understand it. This is what I have I get...

I have the equation \frac{d\rho}{dt}=-\nabla\cdot\rho v where the vector v depends only x and t. I want to take the partial derivative of this whole equation with respect to t. Just not sure how to take the partial of the divergence. Thanks!

Homework Statement Show that n/(n+1)!=(1/n)-(1/(n+1)!) I am totally lost on the algebraic steps taken to come to this conclusion. It is for an Infinite series. Thanks

Homework Statement Find partial fractions for 4/(x^3-2x^2) The Attempt at a Solution Heres the steps that I took: 1. 4/(x^3-2x^2)= 4/(x^2(x-2))= A/(x^2) + B/(x-2) 2. 4= A(x-2) + B(x^2) 3. When x=0, -2A=4, so A=-2, and When x=2, 4B=4, so B=1. 4. So my final answer was: -2/(x^2)+1/(x-2) The...

Homework Statement H(z) = \frac{6-z^{-1}}{1+0.5z^{-1}} + \frac{2}{1-0.4z^{-1}} = k + \frac{A}{1+0.5z^{-1}} + \frac{2}{1-0.4z^{-1}} where A = (6-z^{-1}) is evaluated at z^{-1}=-2. Homework Equations Partial fraction expansion. The Attempt at a Solution Why is z^{-1} set equal to -2? I...

I am curious if there are any issue with commuting the curl of a vector with the partial time derivative? For example if we take Faraday's law: Curl(E)-dB/dt=0 And I take the curl of both sides: Curl(Curl(E))-Curl(dB/dt)=0 Is Curl(dB/dt)=d/dt(Curl(B)) I assume this is only...

Hi, I am not able to understand something about partial tracing. We have a quantum state \rho_{AB}. The Hilbert Space is H_{A}\otimes H_{B}. For some observable A in H_{A}, we have Tr_{A}(\rho_{A}A)=Tr_{AB}(\rho_{AB}(A\otimes 1)) =\sum\sum<a_{j}, b_{k}|\rho_{AB}(A\otimes 1_{B})|a_{j}, b_{k}>...

Homework Statement I had a general inquiry about a relation in my physical chemistry textbook. It stated that when determining the partial pressure of an ideal gas component in a mixture/solution, instead of using the standard Dalton's law: Pi = xiPtot, one can simply use the relation Pi =...

Homework Statement Let F(x,y) be a twice differentiable function such that 4 * Fx2 + Fy2 = 0. Set x = u2 - v2 and y = u*v. Show that Fu2 + Fv2 = 0The Attempt at a Solution Fu = Fx*2u + Fy*v Fv = Fx*-2v + Fy*u Fu2 = 4v2Fx2-4FxFy*u*v+Fy2u2 Fv2 = 4u2Fx2+4FxFy*u*v+Fy2v2 Adding these two...

Hey everyone, I was wondering if someone could help me understand what exactly is happening with a certain integral I am working with, which is as follows: ∫2/(u^2-1)du My steps are as follows (I used partial fractions): ∫(1/(u-1) - 1/(u+1))du = ∫1/(u-1)du - ∫1/(u+1) = ln[(u-1)/(u+1)]...

I was trying to solve this partial differential equation which arose because I wanted to find a general solution to the Laplace equation in the case f=f(x,y). \frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{\partial}^{2}f}{{\partial y}^{2}}=0 Thanks in advance.

Homework Statement So there is an exercise in which I should "verify" the chain rule for some functions. In other words to do it by substitution, then doing by the formula and checking if the results are the same. (and checking with the book`s answer too) For a few of them, they just don`t...

Homework Statement Consider z=sin(x+y+z). This defines z implicitly as a function of x and y. Find an expression for dz/dx The Attempt at a Solution This was on a test, this is what i did. I got 7/11 pts dz/dx = cos(x+y+z)*(1+(dz/dx)) (dz/dx) / (1 + (dz/dx)) = cos(x+y+z) i...

Hi, in general can we tell anything about the partial derivatives of a differentiable function if they are equal? for example I would like them to have to equal some constant. Would this be true?

Homework Statement Calculate the partial derivatives (∂f/∂x & ∂f/∂y) Homework EquationsThe Attempt at a Solution really confusing me with the use of the summation and power to 3/2. This is my attempt, most definitely wrong but still tried. ∂f/∂x = x + c1*(2*(x-x1))*([( x-x1 )^2 +...

Hi guys, I am a Erasmus student in Vienna. Due to the difference between the plans in my home universtity and Vienna, I have to deal with having to take Parcial differential equations without having done Differential Equations 1 or 2. In accordance with my university, I should take here...

Homework Statement Consider the system of equations x^2y+za+b^2=1 y^3z+x-ab=0 xb+ya+xyz=-1 1. Can the system be solved for x, y, z as functions of a and b near the point (x, y, z, a, b)=(-1, 1, 1, 0, 0)? 2. Find \frac{\partial x}{\partial a} where x=x(a, b) The Attempt at a...

Homework Statement w= f(x,y) x = u + v Verify that Wxx - Wyy = Wuv y = u - v Homework Equations The Attempt at a Solution I know how to find Wu or Wv but I have no idea on how to proceed to find the 2nd order derivative (or 3rd,4rth etc.. obviously). I...

Homework Statement I need to prove that x\frac{ \partial^2z}{ \partial x^2} + y\frac{\partial^2z}{\partial y\partial x} = 2\frac{\partial z}{\partial x} Homework Equations z = \frac{x^2y^2}{x+y} The Attempt at a Solution I actually did it the long way and I got the right answer...

Can anyone help with these problems? I have no idea where to start. What is the general approach? Determine the solution of ∂ρ/∂t = (sin x)ρ which satisfies ρ(x,0) = cos x. Determine the solution of ∂ρ/∂t = ρ which satisfies ρ(x,t) = 1 + sin x along x =-2t. Relevant equations: ∂ρ/∂t +...

Homework Statement Find the second partial derivative of v=e^(x*e^y) Homework Equations I know that I need to find Vx and Vy first and then the second partial derivative would be Vxx, Vyy, Vxy. The Attempt at a Solution I'm really confused on how to find Vx or Vy Vx= the...

Homework Statement \int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dx Homework Equations The Attempt at a Solution I've attempted long division, but the long division does not seem to come to an end.. I'm not sure what to make of this.. If the long division does not end, does this mean that...

The question I'm trying to solve is part (ii) of the attached file I've used partial derivatives to input back into the Black Scholes equations and after factorising it, I've got it down to: (a + 2bt + αt +r) * (S².c.e^(at+bt²) = 0 I'm now stuck on what to do next, as there would need to be...

Homework Statement Given F(x_1,x_2,...,x_i,...,x_n) = nth-root(x_1*x_2*...*x_i*...*x_n), how do I take the partial derivative with respect to x_i, where x_i is an arbitrary variable? Homework Equations The Attempt at a Solution Would it just be...

Homework Statement the definite integral of (x-1)/(x^3+4x^2+3x) from x=1 to x=3 using partial fraction decomposition. I know the answer should be (5/3)ln2 - ln3. Homework Equations The Attempt at a Solution After integrating, I got -(1/3)ln(3x) - (2/3)ln(x+3) + ln(x+1) . The...

Homework Statement Stumped. Integral: f(x,y) = ∫ (from 1 to xy) of e^(t^2)dt find both fx and fy The Attempt at a Solution I've come up with: fx(x,y) = ∂/∂x ∫ (from 1 to xy) of e^(t^2)dt Not sure where to go... possibly take the integral, the take the partial derivative? I...

1. The problem statement, all variables and given known data Find the partial derivatives (1st order) of this function: ln((\sqrt{(x^2+y^2} - x)/(\sqrt{x^2+y^2} + x)) Homework Equations The Attempt at a Solution I obviously separated the logarithm quotient into a...

Hi, I have a question regarding partial fractions. One of my Math lecturers said that to find partial fraction, we are actually finding the singularity points. I don't understand what happens at a singularity point that allows us to decompose a function into the sum of two other functions...

Homework Statement Use partial differential calculus to show that if 3 quantities p, V, T are related to each other by some unknown but smooth (which means all derivatives are well defined) equation of state f (P, V, T ) = 0. Then the partial derivatives must satisfy the relation∂p/∂T = - (∂V...

Homework Statement A) if http://www4d.wolframalpha.com/Calculate/MSP/MSP10819hf7feh5hf5hh7e00004ga728h1d42i6h0c?MSPStoreType=image/gif&s=18&w=161&h=20 Find the partial derivatives? B) Suppose you are manufacturing blackboards and whiteboards and that P is your monthly profit when your...

Homework Statement Calculate ∂f/∂s + ∂f/∂t at s = 2, t = -1. Given: f = f(x,y) x = s - t y = s2 + t2 ∂f/∂x (3,5) = 0.06170 ∂f/∂y (3,5) = 0.06170 Homework Equations ∂f/∂s = ∂f/∂x * ∂x/∂s + ∂f/∂y * ∂y/∂s ∂f/∂t = ∂f/∂x * ∂x/∂t + ∂f/∂y * ∂y/∂t The Attempt at a Solution...

Does anyone know how to take the partial derivative of a convolution integral where the derivative is taken with respect to one of the functions of the convolution integral? In the following example, the best I can come up with is: \frac{\partial}{\partial g(t)}\int...

Homework Statement Hello all, New to partial derivatives. I was wondering if someone could look over my work and determine if my final step is as far as I can take the proble (ie. that will be my solution). Thanks in advance. Let the temperature of a 2D domain in polar coordinates (r...

Homework Statement Expand Using Partial Fractions: f(x) = ( 5x-10 )/ ( (x+1)(x-4) ) Involves Integrating afterwards but I don't think this affects my method.Homework Equations This was a question in my mid semester exam, I got the answer correct but he insists my method is wrong.The Attempt at...

I am facing some problem about derivatives in spherical coordinates in spherical coordinates: x=r sinθ cos\phi y=r sinθ sin\phi z=r cosθ and r=\sqrt{x^{2}+y^{2}+z^{2}} θ=tan^{-1}\frac{\sqrt{x^{2}+y{2}}}{z} \phi=tan^{-1}\frac{y}{x} \frac{\partial x}{\partial r}=sinθ cos\phi then \frac{\partial...

Homework Statement This is a bonus problem on our homework, and I'm having trouble figuring out how to setup what I need. Homework Equations Here are my best guesses: f_x=\frac{\partial f}{\partial x} f_y=\frac{\partial f}{\partial y} f_{xx}=\frac{\partial}{\partial...

Homework Statement I'm working a problem, and I've come to taking the derivative with respect to ln(x): \frac{\partial ln(x^{c})}{\partial ln(p_{x})} Homework Equations ln(x^{c})=ln(p^{2}_{y}I)+ln(p_{x}+p_{y})-ln(p_{x})-ln(p_{y}) The Attempt at a Solution I've worked it out...

Homework Statement I am working on a homework problem involving partial derivatives. I've been checking my answers against what Wolfram Alpha spits out just for extra assurance. For the following problem Find all the second partial derivatives: v = \frac{xy}{(x-y)}. When I get to the...

Homework Statement Let \sum_{n=1} a_n and \sum_{n=1} b_n be convergent series. For each n \in \mathbb{N}, let c_{2n-1} = a_n and c_{2n} = b_n. Prove that \sum_{n=1} c_n converges. Homework Equations The Attempt at a Solution Not sure whether the following solution is...

Homework Statement Let f(x,y)=1−x^{2}−y^{2}. Find the point at which \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y} = 0 and illustrate graphically the nature of the surface z = f (x, y) at this point. The Attempt at a Solution Just did the partial derivatives and got...