Partial Definition and 1000 Threads

So figuratively, I'm trying to win a nuclear war with a stick. :smile: I did not take any course in PDEs, I just self-studied some of them, and now I'm toast. :smile: First, please feel free to hurl rocks at me if my simplification is incorrect...

Homework Statement Solve the inhomogenous partial differential equation \frac{∂^{2}u}{∂t^{2}}-\frac{∂^{2}u}{∂x^{2}}=-6u^{5}+(8+4ε)u^3-(2+4ε)u by using the NDSolve function in Mathematica for the interval [0,10] x [-5,5]. Homework Equations Initial conditions: u(0,x)= tanh(x)...

Q3.) Express as partial fractions. a) $$\frac{3x+4}{x^2+3x+2}$$ b) $$\frac{5x^2+5x+8}{(x+2)\left(x^2+2 \right)}$$ c) $$\frac{x^2+15x+21}{(x+2)^2(x-3)}$$

Homework Statement Find an equation for the path of a particle that starts at P(10,10) and always moves in the direction of maximum temperature increase if the temperature in the plane is T(x,y) = 400-2x^2 -y^2 Homework Equations T(x,y) = 400-2x^2 -y^2 dT/dx = -4x dT/dy = -2y...

Here is the question: I have posted a link there so the OP can view my work.

http://en.wikipedia.org/wiki/Partial_fraction_decomposition In general, if you have a proper rational function, then: if ## R(x) = \frac {P(x)}{Q(x)} ## and ## Q(x) = (mx + b)^n ... (ax^2 + bx + c)^p ## where ##Q(x)## is composed of distinct linear powers and/or distinct irreducible...

Homework Statement Show that a relation of the kind ƒ(x,y,z) = 0 then implies the relation (∂x/∂y)_z (∂y/∂z)_x (∂z/∂x)_y = -1 Homework Equations f(x,y) df = (∂f/∂x)_y dx + (∂f/∂y)_x dy The Attempt at a Solution I expressed x = x(y,z) and y = y(x,z) then found dx and...

Hello all, I am trying to calculate the second order of the partial derivative by x of the function: f(x,y)=(x^2)*tan(xy) In the attach images you can see my work. Both the answer in the book where it came from and maple say that the answer is almost correct, but not entirely. In the last...

Homework Statement I'm taking the Laplace transform of F(s), and the first thing is to expand it by partial fraction or something so that I can match F(s) with a table of laplace transforms. Homework Equations The Attempt at a Solution Does partial fraction even work? I've got two...

Ok folks, I've taken a stab at the Latex thing (for the first time, so please bear with me). I've mentioned before that I'm teaching myself relativity and tensors, and I've come across a question. I have a few different books that I'm referencing, and I've seen them present the ordinary...

Homework Statement z = x^2 +y^2 x = rcosθ y = rsinθ find partial z over partial x at constant theta Homework Equations z = x^2 +y^2 x = rcosθ y = rsinθ The Attempt at a Solution z = 1 + r^2(sinθ)^2 dz/dx = dz/dr . dr/dx = 2(sinθ)^2r/cosθ = 2tanθ^2x...

Hi everyone! I'm not sure if this is the right forum to post my question. If I'm wrong, let me know it. The question: Let us consider the functions \theta=\theta(x,y), and M=M(\theta), where M is a operator, but i doesn't relevant to the problem. I need to know the derivative \frac{\partial...

Homework Statement Well this is part of an integration process, namely: \int \frac {sin^2x}{4+3cos^2x}dx Homework Equations My attempt involved using a u-substitution, namely t = tan x The Attempt at a Solution Using t = tan x, sin^2 x = \frac {t^2}{1+t^2} and cos^2 x = \frac...

Is there a derivation for ∂f(x,y)/∂x given: f(x,y): g(x,y)h(x,y) e.g. sin(x)(x+2y)

Homework Statement Hi Say I have a function f(x(t), t). I am not 100% sure of the difference between \frac{df}{dt} and \frac{\partial f}{\partial t} Is it correct that the relation between these two is (from the chain rule) \frac{df}{dt} = \frac{\partial f}{\partial t} +...

Hello there, This isn't specifically homework, it is study. I'm having a difficult time trying to understand how to calculate/estimate partial decay widths, \Gamma[\itex], and Branching Ratios. I haven't found very clear information online so far. Here's just an example below that I'd like...

Homework Statement let V=f(x²+y²) , show that x(∂V/∂y) - y(∂V/∂x) = 0 Homework Equations The Attempt at a Solution V=f(x²+y²) ; V=f(x)² + f(y)² ∂V/∂x = 2[f(x)]f'(x) + [0] ∂V/∂y = 2[f(y)]f'(y) I'm sure I've gone wrong somewhere, I have never seen functions like this...

Homework Statement Suppose we have a mixture of the gases H2, CO2, CO and, H2O at 1200 K, with partial pressures pH2 = 0.55 bar, pCO2 = 0.2 bar, pCO = 1.25 bar, and pH2O = 0.1 bar. Is the reaction described by the equation CO + H2O <=> H2 + CO2 at equilibrium under these conditions? If not...

For spherical coordinates, u(r,\theta,\phi) is function of r,\theta,\phi. a is constant and is the radius of the spherical region. Is: \int_{0}^{2\pi}\int_{0}^{\pi}\frac{\partial\;u(r,\theta,\phi)}{\partial {r}}a^2\sin\theta d\theta d\phi=\frac{\partial}{\partial...

Hello, I am not completely certain why in thermodynamics, it seems that everything is done as a partial derivative, and I am wondering why? My guess is because it seems like variables are always being held constant when taking derivatives of certain things, but it is still somewhat a mystery to...

Hi I have a question about partial derivatives? For example if I have a function x = r cos theta for all functions, not just for this function will dx/d theta be the inverse of dtheta/dx, so 1 divided by dx/d theta will be d theta/ dx? Please help on this partial derivative question...

I got x = (u2 - v2) / u y = (v2 - u2) / v I differentiated them w.r.t u & v respectively & solved the given equation but I'm not getting the answer which is 0. Please view attachment for question!

Homework Statement let u=f(x,y) , x=x(s,t), y=y(s,t) and u,x,y##\in C^2## find: ##\frac{\partial^2u}{\partial s^2}, \frac{\partial^2u}{\partial t^2}, \frac{\partial^2u}{\partial t \partial s}## as a function of the partial derivatives of f. i'm not sure I'm using the chain rules...

I was working on a pde, and I needed to compute a Jacobian for it. Suppose we have a function consisting of a series of matrices multiplied by a vector: f(X) = A * B * b --where X is a vector containing elements that are contained within A, b, and/or b, --A is a matrix, B is a matrix, and b is...

Here are the questions: I have posted a link there to this thread so the OP can see my work.

Se a function f(x(t, s), y(t, s)) have as derivative with respect to t: \frac{df}{dt}=\frac{df}{dx} \frac{dx}{dt}+\frac{df}{dy} \frac{dy}{dt} And, with respect to s: \frac{df}{ds}=\frac{df}{dx} \frac{dx}{ds}+\frac{df}{dy} \frac{dy}{ds} But, how will be the derivative with respect to...

Homework Statement If you sum this from one to infinity. Ʃ (cos(1/(n)^2 - cos(1/(n+1)^2) Homework Equations The Attempt at a Solution Ʃ (cos(1/(n-1)^2 - cos(1/(n+1)^2) This is telescoping if you work that out for the partial nth partial sum you get cos(1) -...

Homework Statement http://i.minus.com/jbzyIAyMvUrADW.png Homework Equations Conservation of mass in a closed system. The Attempt at a Solution I'm not sure what the lecture is getting at here. Why is it that the number of moles of NO2 added to twice the number of moles of N2O4...

Homework Statement ∫▒√(1+x^2 )/x dx Homework Equations The Attempt at a Solution I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.

Homework Statement A mixture of He, Ne, and Ar has a total pressure of 0.80 atm and is found to contain 0.55 mol He, 0.94 mol Ne, and 0.35 mol Ar. What is the partial pressure of each gas in atm? Homework Equations Partial pressure for a gas is equal to the mole fraction of the gas...

Hello Everyone, So in other words, if you didn't understand what I'm saying from the title of this post, look at it this way: What is the answer to this integral? ∫(partial dx)/(partial dt) * dx According to my textbook the answer is 0 but I'm getting easily confused as to how this is...

Hello everyone, I have read about the theoretical values of the Z boson decay partial width and how well they agreed with experiment. However there is something I do not quite understand: since these theoretical calculations were performed with the hypothesis that the masses of the decay...

Given a function: z(x,y) = 2x +2y^2 Determine ∂x/∂y [the partial differentiation of x with respect to y], Method 1: x = (z/2) - y^2 ∂x/∂y = -2y Method 2: ∂z/∂x = 2 ∂z/∂y = 4y ∂x/∂y = ∂x/∂z X ∂z/∂y = (1/2) X 4y = 2y One or both of these is wrong. Can someone point out...

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 [FONT=times new roman]u(x,y) given by [FONT=arial] [FONT=times new roman]yux - 3x2 uy = 0 [FONT=times new roman].I try [FONT=times new...

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...