Partial Definition and 1000 Threads

How do I go about solving a differential equation of the form \partial_{x}F_{x}(x,y) + \partial_{y}F_{y}(x,y) = g(x,y) Where g(x,y) is a known function and I wish to solve for F. I thought i could apply the method of characteristics but the characteristic equation is dependent on coefficients...

Hi I need help regarding following can I write following partial derivative wrt x multiplied by Ax (∂A[x])Ax =∂(Ax^2)

[b] Homework Equations N/a The Attempt at a Solution I am wondering if this is the right direction in solving this. any input would be great! Sorry for the messy handwriting!

Hi all , I would like to solve the following partial differential equation. (∂α/∂t)=G[sub(α)] *(a'-a) I attached the equation and solution here as an image. I don't know how it was derived. I hope someone can help me

Homework Statement To find the decomposition of a polynomial with a repeated factor in the denominator, you should separate them into (x+a)^1 + ... + (x+a)^n. But, my question is why? For example, why should you decompose it in the following way: \frac{x+2}{(x+1)(x+3)^2} = \frac{A}{x+1}...

Homework Statement Find (\frac{dV}{dp})_{n,T} for the Van de Waals gas law Homework Equations Van de Waals gas law: (\frac{p+an^2}{V^2})(V-nb)=nRT The Attempt at a Solution I just started doing problems like these so I would like to know if I am doing them right... What I did was I took...

Hi. Assume there's a probability ##q## for a guy to take a step to the right, and ##p=1-q## to take one to the left. Then the probability to take ##n## steps to the right out of ##N## trials is ##P(n) = {{N}\choose{n} }q^n p^{N-n}##. Now, what is ##<n>##? My textbook in statistical physics...

Please help me with this, In Reheat Rankine cycle, we first Expand the steam partially in a high pressure turbine and then reheat it again . How is this partial expansion in high pressure turbine done ? in the sense, what is the procedure followed to have only partial expansion of steam...

can anyone tell me the difference of application of total derivative and partial derivative in physics? i still can't figure it out after searching on the internet

many books only tell the operation of total derivative and partial derivative, so i now confuse the application of these two. when doing problem, when should i use total derivative and when should i use partial derivative. such a difference is detrimental when doing Physics problem, so i...

1. Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0 mL steel vessel at 0 °C, the pressure is 0.229 atm. When the vessel and its contents are warmed to 100 °C, Q decomposes into its constituent elements. What is the total pressure, and what are the partial...

Homework Statement Doing a homework question and I ran it through wolfram and I get a different answer to what I'm working it out as...and I can't see where I'm going wrong. Anyone able to give a pointer? my equation is \frac{1}{s(0.641s + 1)} Wolfram gives the answer as...

I always see people when doing partial fraction decomposition just plug in arbitrary values of x to cancel out some constant terms like A,B,C in order to solve it. I just want to know how this works. I've heard that since A,B, and C are constants it has to hold true for any values of x(like a...

Homework Statement H2(g) + S(s) = H2S(g) Kc= 6.8x10^-2 If 0.2 moles of H2 and 1.0 mole of S are heated in a 1L vessel upto 90C, what will be the partial pressure of H2S at equilibrium? Can someone help me with this step by step?Homework Equations The Attempt at a Solution Kc = 6.8X10^-2 = x /...

Homework Statement Given f(x, y, z) = 0, find the formula for (\frac{\partial y}{\partial x})_z Homework Equations Given a function f(x, y, z), the differential of f is df = \frac{\partial f}{\partial x}dx + \frac{\partial f}{\partial y}dy + \frac{\partial f}{\partial z}dz...

Homework Statement If xs^2 + yt^2 = 1 and x^2s + y^2t = xy - 4 , find \frac{\partial x}{\partial s}, \frac{\partial x}{\partial t}, \frac{\partial y}{\partial s}, \frac{\partial y}{\partial t} , at (x, y, s, t) = (1, -3, 2, -1) Homework Equations The Attempt at a Solution I...

Alright, I am here again with another question... When I have a rational function, let's say (x+4)/(x-2)(x-3) I rewrite it like A/(x-2) + B(x-3) and then solve it for A & B. But when we have for e.g (x^2 + 3x + 2)/(x(x^2 +1 )) the book tells me to rewrite it like: A/x + (Bx + C)/(x^2 + 1)...

Homework Statement On a planet not entirely unlike earth, the ratio of the partial pressure of N2 to that of O2 equals 1 at an altitude of 1 km: \frac{p_{\text{N}_2}}{p_{\text{O}_2}} = 1. Assuming that T = 200 K, and the gravitational constant is 5 m/s2, what is the ratio...

Homework Statement The problem and solution are attached as TheProblemAndSolution.jpg. I will also copy down the problem and solution here.: Problem: Consider the set ℤ of integers. Define aRb by b = a^r for some positive integer r. Show that R is a partial order on ℤ, that is, show that...

$$\int \frac{7dx}{x(x^2+8)^2}$$ so I am thinking its going to be set up like: $$\frac{A}{x} + \frac{Bx + C}{x^2 + 8} + \frac{Dx + E}{(x^2 + 8)^2}$$ Practice problem I'm stuck on. so I cleared fractions and got A = 7/64 , b = -7/64 and C = 105/64 and now I'm lost... can anyone work this problem...

Homework Statement Find the partial fractions for this expression. (((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1))) The Attempt at a Solution The final answer is 1/sqrt(n) - 1/(sqrt(n+1)) My work: A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n)) I am subbing in n = -1 and n = 0 to solve for...

Without being too concerned how we got there. The answer to a partial fraction question a friend and I are doing is 24/5 ln(2) - 8/5ln(3) The system does not accept this answer however, it wants the simplified form 8/5 ln (8/3) We're not sure how to get that form. More specifically 8/5...

I'm a little rusty with partial fractions, and I can't seem to find my error once I get up to that point. Homework Statement dy/dx = (y^2 - 1) / x Homework Equations The Attempt at a Solution Cross-mutliply x dy = (y^2 - 1) dx Divide by the appropriate terms dy / (y^2...

Hey guys, Here is another pair of questions that I'm doubting at the moment: I used partial fractions for A and got (Bx+C)/x^2 + Ax/(x-1)^2 + Dx(x-1) which led me to compute A=1, B=0, C= -1, and D=0, which already sounds off. Do you guys have any suggestions? Also, for 5b, I calculated B=...

Homework Statement Evaluate the integral. (Remember to use ln |u| where appropriate. Use C for the constant of integration.) \int \frac {5x^2 - 20x +45}{(2x+1)(x-2)^2}\, dx Homework Equations 5x^2 - 20x +45 = 5 (x^2 -4x +9) The Attempt at a Solution I'm able to come up with an...

First the example problem. This is an integral of the whole thing (3x^3+24x^2+56x-5) / (x^2+8x+17)^2 The answer comes out to be 3/2 ln(x^2+8x+17) - (49/2 tan^-1(x+4)) - (25x+105 / 2(x^2+8x+17) + C I would show all the steps but I'm still not sure on how to use the format tools, so that...

I just need some clarification that this is fine so I have f_{x} = -2xe^{-x^2-y^2}cos(xy) -ysin(xy)e^{-x^2-y^2} now, taking the second derivative f_{xx} = [-2xe^{-x^2-y^2}+4x^2e^{-x^2-y^2}]cos(xy) - ysin(xy)[-2xe^{-x^2-y^2}]+2xe^{-x^2-y^2}sin(xy)y-cos(xy)e^{-x2-y^2}y^2

I know how to prove this via limits and I'm okay with that. What I want to understand is the interpretation of the theorem and specifically a visualisation of why what the theorem states must be the case. My guess is that this theorem is saying that change is symmetrical. But I don't know...

Hey guys, I'd really appreciate it if I could get some quick help for this problem set I'm working on. For question one, I just did a quick u substitution for x^4 and managed to get x^4 * sin(x^4)+cos(x^4) + C. For part b, I used integration by parts and took ln(4t) as u and the rest as...

There is a device called a Fizz Keeper that attaches to carbonated beverage bottles and is supposed to keep them from going flat after they are opened by pressurizing them with air. Dalton's law and Henry's law have been used to debunk the device as ineffective. The argument against the...

1. Marine biologists have determined that when a shark detects the presence of blood in the water, it will swim in the direction in which the concentration of the blood increases most rapidly. Suppose that in a certain case, the concentration of blood at a point P(x; y) on the surface of the...

Let's say we have a function F(\vec{r})=F(s, \phi, z). Then (correct me if I'm wrong): \frac{dF}{dx}=\frac{\partial F}{\partial s}\frac{ds}{dx}+... So then what is \frac{\partial F}{\partial x}? Is it zero because F doesn't depend explicitly on x? Is it the same as \frac{dF}{dx}=\frac{\partial...

Find the partial fraction decomposition for the rational function. $$\frac{-4x^2 - 8x - 19}{(x^2 + 2)(x-9)}$$ I'm not sure what to do.

Hello! This is my first post to this excellent forum! I would like some help with this exercise: u_{xx} (x,y) + u_{yy} (x,y) = 0, with 0 < x < 2 \pi , 0 < y < 4 \pi u_x (0,y) = 0, \, u_x(2 \pi, y) = 0, \, 0< y < 4 \pi u(x,0) = a \cos(2x), \, u(x, 4 \pi) = a \cos^3(x), \, 0<x<2\pi...

This semester I'm a bit stuck with classes to progress my Electrical Engineering major (having going into it so late), so the only class I can take to progress is a physics course about electricity and the likes. I need at least a three unit class in order to get at least half time so I won't...

Homework Statement Solve PDE ##\frac{\partial u}{\partial t}-k\frac{\partial^2 u}{\partial x^2}=0## for ##0\leq x \leq \pi ## and ##t\geq 0##. Also ##\frac{\partial u}{\partial x}(0,t)=\frac{\partial u}{\partial t}(\pi ,t)=0## and ##u(x,0)=sin(x)##.Homework Equations The Attempt at a Solution...

Hey I am currently studying Quantum Mechanics and I have difficulty grasping a concept. I don't understand the following step in the derivation: \langle X_{A} \rangle=tr\left[\left(X_{A}\otimes I_{B}\right)\rho_{AB}\right] =tr_{A}\left[X_{A} tr_{B}\left[\rho_{AB}\right]\right] Thanks

Homework Statement For the equation shown below: x2+2x+3 / (x2+9)(X-3) = Ax+B/(x2+9) + C/(x-3) Find A, B and C Homework Equations The Attempt at a Solution C = 1 B = 2 A = ? Find C which = 1 by putting x=3 and working out x2+2x+3/(x2+9), then multiply out equation...

Hello! :) From the relations: $$\partial_{r}=\cos \theta \cdot \partial_{x}+ \sin \theta \cdot \partial_y$$ $$\partial_{\theta}=-r \sin \theta \cdot \partial_x+ r \cos \theta \cdot \partial_y$$ we get: $$\partial_y=\sin \theta \cdot \partial{r}+\frac{\cos \theta}{r} \cdot \partial_{...

Hello. Can someone check if my partial derivatives are correct? I am not so confident with my answers.

Hello, i've come across a partial fractions problem that I don't know how to solve - Usually, the denominator of the fraction I need to split up into two separate fractions is a quadratic, but in this instance it's a cubic. Specifically, the problem I'm having is that two of the factors to...

Any books that are easy to understand on partial differential equations? I just came back from barnes and noble. I briefly looked at the book on partial differential equations, but it is confusing for me because it jumps to topics about partial differentiation that I didn't learn. The only...

Homework Statement I have to find a natural number N that satisfies this equation: \sum^{N}_{i=1} \frac{1}{i} > 100 Homework Equations I tried finding a close form of the sum but couldn't find anything useful. The Attempt at a Solution Well after trying some numbers in maple I...

Homework Statement Find the indefinite integral of the below, using partial fractions. \frac{4x^2+6x-1}{(x+3)(2x^2-1)} Homework Equations ?The Attempt at a Solution First I want to say there is probably a much easier and quicker way to get around certain things I have done but I have just...

I've seen it written two different ways: $$\frac{\partial f}{\partial x} = \lim\limits_{h \rightarrow 0} \frac{f(x + h, y) - f(x,y)}{h}$$ and $$\frac{\partial f}{\partial x} = \lim\limits_{h \rightarrow 0} \frac{f(x_0 + h, y_0) - f(x_0,y_0)}{h}$$ where the latter evaluates the function at...

Given V=xf(u) and u = \frac{y}{x} How do you show that: x^2 \frac{\partial^2V}{\partial x^2} + 2xy\frac{\partial^2V}{\partial x\partial y} + y^2 \frac{\partial^2V}{\partial y^2}= 0 My main problem is that I am not sure how to express V in terms of a total differential, because it is a...

System of PDEs--Heat Equation For Two Objects Hello everyone, Before is a system of partial differential equations; to be specific, it is this system: \frac{\partial U_A }{\partial t} = - \frac{k_B}{k_A} \alpha_A \left( \frac{\partial^2 U_B}{\partial x^2} + \frac{\partial^2 U_B}{\partial...

Homework Statement Ammonia gas decomposes to nitrogen and hydrogen spontaneously with an equilibrium constant, Kp = 5.9 x 109. Calculate the partial pressure of ammonia at equilibrium given that the partial pressure of nitrogen and hydrogen are both 2.7 atm initially. [Hint: If you need...

if U = sin^-1 (x/y) +cos(y/x) then Ux/Uy = ? ans is -y/x. i have specially doubt on the partial derivative of U w.r.t y for inverse sin. thank you in advance

Homework Statement if z = x2 + 2y2 , x = r cos θ , y = r sin θ , find the partial derivative [SIZE="4"]\left(\frac{\partial z}{\partial \theta}\right)_{x} Homework Equations z = x2 + 2y2 x = r cos θ y = r sin θ The Attempt at a Solution The textbook says that the equation...