Partial Definition and 1000 Threads

Homework Statement Why when I try to evaluate this with Partial Fractions, why do I end up with the original function? \int\frac{n}{(n^{2}+1)^{2}} \frac{n}{(n^{2}+1)(n^{2}+1)} \frac{Ax+B}{n^{2}+1} + \frac{Cx+D}{(n^{2}+1)^{2}} 1n = (An+B)(n^{2}+1) + Cx + D 0n^{3}+ 0n^{2} + 1n + 0n^{0} =...

I just want to verify For Polar coordinates, ##r^2=x^2+y^2## and ##x=r\cos \theta##, ##y=r\sin\theta## ##x(r,\theta)## and## y(r,\theta)## are not independent to each other like in rectangular. In rectangular coordinates, ##\frac{\partial y}{\partial x}=\frac{dy}{dx}=0## But in Polar...

Hi I'm having a bit of trouble with this question: Use separation of variables to find all the possible separable solutions to the partial DE equation for u(x,y) given by yux - 3x2 uy = 0 .I try u= X(x) Y(y) ux = X'(x) Y(y) uy = X(x) Y'(y) which gives y(X' Y)-3x2(X Y') then I divide by...

I need to solve the following system of equations for n=0,1,2 subject to the given initial and boundary conditions. Is it possible to solve the system numerically. If yes, please give me some idea which scheme I should use for better accuracy and how should I proceed. The coupled boundary...

For polar coordinates, ##u(x,y)=u(r,\theta)##. Using Chain Rule: \frac{\partial u}{\partial x}=\frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial u}{\partial \theta}\frac{\partial \theta}{\partial x} The book gave \frac{\partial ^2 u}{\partial x^2}=\frac{\partial...

Homework Statement using the method of separation of variables, solve ∂u/∂x=4∂u/∂y, where u=3e^-y - e^-5y when x=0. Homework Equations The Attempt at a Solution let u(x,y)=X(x)Y(y) =XY.

can anyone direct me to a website that gives adequate treatment of the numerical solution of partial differential equations, especially pertaining to problems which involve the use of the Crank-Nicolsen procedure?

Hi all, I've got a question regarding a price elasticity problem and a partial derivative. That's what's given for the exercise: So, first of all we calculate all the demand with the given information. Which is: And then we come to the actual problem. (4. b) ) How do they...

Homework Statement Show that: Ʃ(-1)n/(n^2+a^2) (from n=0 to ∞) = pi/[asinh(pi*a)], a\neq in, n\in Z. Homework Equations f(z) = f(0) + Ʃbn(1/(z-an)+1/an) (from n=1 to ∞) , where bn is the residue of f(z) at an. The Attempt at a Solution The main problem is I don't how to pick the...

Solve ##au_{x} + bu_{y} = f(x,y)##, where ##f(x,y)## is a given function. If ##a \neq 0##, write the solution in the form $$u(x,y) = (a^{2} + b^{2})^{\frac{-1}{2}} \int_{L} f ds + g(bx - ay)$$ (from Partial Differential Equations An Introduction, 2nd edition by Walter A. Strauss; pg. 10) I...

Homework Statement Let W = F(u(s,t),v(s,t)) (in my notation, u_s would represent du/ds u(1,0) = -7 v(1,0) = 3 u_s(1,0)=8 v_s(1,0)=5 u_t(1,0)=-2 v_t(1,0)=-4 F_u(-7,3)=-8 F_v(-7,3)=-2 Find W_s(1,0) and W_v(1,0) Sort of having a hard time getting started here... I believe...

could someone show me how \frac{∂}{∂t}(\frac{∂z}{∂u})= \frac{∂^2z}{∂u^2} \frac{∂u}{∂t} where z=z(u) u=x+at

Homework Statement Solve \frac{\partial{w}}{\partial{t}} + c \frac{\partial{w}}{\partial{x}} =0 \hspace{3 mm} (c>0) for x>0 and t>0 if w(x,0) = f(x) w(0,t) = h(t) Homework Equations The Attempt at a Solution I know how to solve for the conditions separately and that would give...

Homework Statement ∫(x+1)/(x2+2x+3)dx The Attempt at a Solution This problem was under partial fractions in my book. I solved it using u-substitution where u=x2+2x+3, but i can't see how it can be solved using partial fractions? can it?

Homework Statement f(t) a continuously differentiable function twice over the circle T1 cr its Fourier coefficients and σn(f,t) partial sum of Fejer. a.Demonstrate that http://imageshack.us/a/img94/5992/ds35.png b. Consider k as -n≤k≤n , using cr coefficients calculate...

Homework Statement The function given is (1+xz)^(1/2) + (1-xy)^(1/2) I have to take the partial derivative with respect to x, y, and z. The question says Choose the order wisely. I don't understand what it means? How could I choose the order badly? Can anyone skilled in explaining math to...

Homework Statement ∫ 4x/(x^3+x^2+x+1) dxThe Attempt at a Solution I really don't know where to start, you can't complete the square, the degree of the numerator is less than the denominator so you can't use long division to simplify it. I can't really simplify the denominator as well, so I...

Homework Statement \frac{\partial f}{\partial t},\frac{\partial f}{\partial x} where f=f(x,t,\frac{dx}{dt}) Homework Equations The Attempt at a Solution I think it's impossible to consider it as a simple partial derivative.

Homework Statement Find the first partial derivatives ∂z/∂x and ∂z/∂y of sin(0x+5y+z)=0 at (0,0,0). Homework Equations sin(0x+5y+z)=0 The Attempt at a Solution 0x+5y+z=kπ z=kπ-5y So, ∂z/∂x= 0 and ∂z/∂y= -5 What I do not understand is WHY 0x+5y+z=kπ is an acceptable...

The question is: a) Find explicit expressions for an ideal gas for the partial derivatives: (∂P/T)T, (∂V/∂T)P and (∂T/∂P)V b) use the results from a) to evaluate the product (∂P/V)T*(∂V/∂T)P*(∂T/∂P)V c) Express the definitions of V(T,P) KT(T,P)an BT(T,V) in terms of the indicated independent...

My professor asks us to solve the integral of: [x/(x^4 + 1)]dx This expression is not factorable; what should I do? She is asking us to solve specifically using PFD, not u-substitution.

I have a function Z = f(P,T) and would like to calculate the partial differentials \left ( \frac{\partial Z}{\partial P} \right )_T and \left ( \frac{\partial Z}{\partial T} \right )_P at values of P and T. The function Z is compressibility factor (Lee and Kessler equation of state), P...

Homework Statement At 1 atm of pressure a volume of 22 liters of N2 gas is passed in a closed system over a boat containing Hg liquid at 100°C. The flow of N2 is slow to allow the gas to become saturated with mercury. At 20°C and 1 atm, the nitrogen was found to contain 0.0647g of Hg...

Here is the question: Here is a link to the question: Integral of ((19x^2)-x+4)/(x(1+4(x^2)))? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Question 2 from http://math.berkeley.edu/~mcivor/math53su11/solutions/hw6solution.pdf here. I do not understand b) and e). How do I think of the slope with respect to y? Homework Equations The Attempt at a Solution I do know that the partial derivatives are...

Homework Statement suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1 Homework Equations Sn= (-2n+9)/(6n+15 The Attempt at a Solution So I attempted to subtract S(n-1) from S(n) to get each...

Homework Statement Write out the form of the partial fraction decomposition of not determine the numerical values of the coefficients. Homework Equations x^4 -2x^3 + x^2 +2x -1 / x^2 -2x +1 The Attempt at a Solution I did the division and I got x^2 + ((2x-1)) / (x^2 -2x +1)...

Hey guys, i have read many posts on physics forums but this would be my first post. I am quite stuck so any help would be much appreciated. Homework Statement Use Laplace transforms to solve the initial value problem: f''(y) + 4f'(y) +8y = u(t-1) where y(0) = 1 and y'(0) = -1 Solve...

Greetings, In Griffiths E&M, 3rd. Ed., on page 214, the following is part of the derivation of the continuity equation (the same derivation is shown on the Wikipedia article for the current density, under the continuity equation section: http://en.wikipedia.org/wiki/Current_density)...

I am a bit confused about a question on proving partial order relation. here is the question and what i done so far. "define the relation '≤' on a boolean algebra B by for all x,yεB x≤y if and only if xVy=y, show that '≤' is a partial order relation" first of all what exactly does...

Homework Statement If ##z=x\ln(x+r)-r## where ##r^2=x^2+y^2##, prove that $$\frac{∂^2z}{∂x^2}+\frac{∂^2z}{∂y^2}=\frac{1}{x+y}$$Homework Equations The Attempt at a Solution Since ##r^2=x^2+y^2##, ##∂r/∂x=x/r## and ##∂r/∂y=y/r##. Differentiating z w.r.t x partially...

Hi everyone, Z=y+x^2*y+x^2+x^3+x^4+5 I would like to find the partial derivative of: diff(z,x) ? diff(z,y)? Kindly give me a step by step solution. Hope to hear from you soon. Thanking you all in advance for your replies.

Homework Statement ∫(2e^x)/(e^(2x)-1)dx Homework Equations The Attempt at a Solution I was told to solve using partial fractions. When I set up the partial fraction I got: A/e^x+1 + B/e^x-1 = 2e^x When I broke it up, I solved for A and B and got that A and B should both...

[b]1. Homework Statement [/b Here is a question on proof of partial correctness with 2 while loops with Hoare logic {True} z:=1 m:=x n:=y while (n=!0) do while (even(n)) do m:=m*n n:=n/2 n:=n-1 z:=z*m {z=x^y} Homework Equations The Attempt at a Solution I...

Is \frac{∂y}{∂x}×\frac{∂x}{∂z}=-\frac{∂y}{∂z}?

I am given Z = f (x, y), where x= r cosθ and y=r sinθ I found ∂z/∂r = ∂z/∂x ∂x/∂r + ∂z/∂y ∂y/∂r = (cos θ) ∂z/∂x + (sin θ) ∂z/∂y and ∂z/∂θ = ∂z/∂x ∂x/∂θ + ∂z/∂y ∂y/∂θ= (-r sin θ) ∂z/∂x + (r cos θ) ∂z/∂y I need to show that ∂z/∂x = cos θ ∂z/∂r - 1/r * sin θ ∂z/∂θ and ∂z/∂y = sin...

Hi, I was reading something on conservative fields, in this example \phi is a scalar potential. (Please refer to the attatched thumbnail). It's partial derivatives, but I'm not sure why the d\phi/dx * dx, the dx should cancel out? and that should leave d\phi. So the integral should be -3∫d\phi...

I got 2 questions to ask! I have finished one but not sure if it's correct so I need to double check with someone :) http://imageshack.us/a/img708/1324/83u8.png Here is my worked solution, I took this picture with my S4 and I wrote is very neatly as I could! The reason I didn't type it all...

I'm having problem with task (a) in this problem The question My attempt The solution Why don't I get the same after I take the partial fraction using my calculator? And where does this R(s)=1/s^2 come from

What math subject comes after partial differential equations for physics and electrical engineering majors?

Is partial derivative of ##u(x,y,z)## equals to \frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}+\frac{\partial u}{\partial z} Is partial derivative of ##u(r,\theta,\phi)## in Spherical Coordinates equals to \frac{\partial u}{\partial r}+\frac{\partial u}{\partial...

I am venturing in the realm of probability and I came across a concept that I call partial dependence. IE, it is a set of a events which a neither independent nor dependent on each other. They fall somewhere "in between". I have looked on the internet and I really don't understand the...

Hi, I am sort of hung up with a particular step in a derivation, and this has caused me to ponder a few properties of partial derivatives. As a result, I believe I may be correct for the wrong reasons. For this example, the starting term is (\frac{\partial}{\partial x}\frac{\partial...

Hello, the question I have arises from the 4th Edition of the book "Advanced Engineering Mathematics" written by K.A. Stroud. For those who owns the book, it is the example #2 starting at page 379. More precisely, the example is separated into two parts but the first one is very straight...

Homework Statement I found this solved example in an old textbook. I don't think that the solution provided is correct. I'll be very grateful if someone could verify it. Question: xxyyzz = c What is \frac{∂z}{∂x}? Solution Provided: Taking logarithms on both sides: zlog(z) =...

My understanding is that when a fan begins spinning, a partial vacuum is created. Physically, what creates this partial vacuum? Does the motion of the blades create a void in which there are fewer air molecules than in the ambient air and thus the pressure is lower than the ambient pressure?

Hi, As I understand it, if you have a piece of matter (hydrogen) and a piece of antimatter (anti-hydrogen) and they interact with each other they annihilate. What if your matter was Helium and your "antimatter" was anti-hydrogen? or the other way around what if your antimatter was antihelium...

Homework Statement Find Partial Fraction Decomposition of ##(x^4 - 1) / (x^3 + x^2 + x)## Homework Equations The Attempt at a Solution ##(x^4 - 1) / (x^3 + x^2 + x) = (x^4 - 1) / (x)(x^2 + x + 1) = A/x + B/(x^2 + x + 1)## ##(x^4 - 1) = A(x^2 + x + 1) + B(x)## ##(x^4 - 1) = Ax^2 + Ax...

Suppose I have some function f that depends on three variables, namely x, y, and t; i.e., f=f(x,y,t). Now suppose that y depends on x, i.e., y=y(x). Taking this into account, we see that f is really just a function of two independent variables, x and t. So my question is this: if I write down...

Homework Statement Consider the series Ʃ 1/[k(k+2)]; n=1 to infinity Find the formula for the partial sum Sn 2. The attempt at a solution I have calculated the first 5 terms of the sequence as follows, but I can't see any pattern. Am I doing this right? S1=1/3 S2=1/3+1/8=11/24...