Partial Definition and 1000 Threads

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...

The humidity level is 80% and T=303Kelvin. So I can use the equation RH = Pw/Pws to calculate the Pw = Partial pressure of water vapor, by finding Pws with the following equation: Pws=e^(77.3450+0057T-7235/T)/T^8.2 = 4200Pa, where T is in Kelvin. So Pw=0.8*4200Pa=3360Pa I can find Pa by...

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?

Write a partial sum for the power series, URGENT Consider the function ln(1+4x). Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were Sigma from n=0 to infinity of 3^nx^2n , you would write...

Hi, I am a master student comes from USM in Malaysia. My main focus is on monopole instanton solution in static form which did not include time, i using the Lagrangian to generate out the 12 set equations of motion with 8 variables, the software that i use is Matlab with Optimization toolbox-...

Hello. I have equation: \frac{\partial T}{\partial t}-\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0 I calculated determinant: \Delta=(-\frac{1}{2})^2)-4\cdot 1 \cdot 0 \Rightarrow \sqrt{\Delta}=\frac{1}{2} \\ (\frac{dT}{dt})_{1}=-\frac{1}{4} \\ (\frac{dT}{dt})_{2}=\frac{1}{4} next...

Homework Statement Demonstrate that C_{Y,N}=\left ( \frac{ \partial H}{\partial T } \right ) _{Y,N} where H is the enthalpy and Y is an intensive variable. Homework Equations (1) C_{Y,N}=\frac{T}{N} \left ( \frac{ \partial S}{\partial T } \right ) _{Y,N} (2) T= \left ( \frac{ \partial...

Homework Statement Okay, so here's the problem: (a) Let U be a universal set and suppose that X,Y\in U. Define a relation,\leq, on U by X\leq Y iff X\subseteq Y. Show that this relation is a partial order on U. (b) What problem occurs if we try to define this as a relation on the set...

Homework Statement I have this lowpass circuit which I have transformed to the S-domain. The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain. Here's the transfer function of the lowpass circuit: H(s) = \frac{\frac{1}{LC}}{s^2 +...

As part of a project I have been working on I fin it necessary to manipulate the following expression. e^(icx)/(x^2 + a^2)^2 for a,c > 0 I would like to decomp it into the form A/(x^2 + a^2) + B/(x^2 + a^2) = e^(icx)/(x^2 + a^2)^2 but I am having trouble getting a usable outcome.

I'm have a little trouble understanding PA=LU, I have no problems with A=LU but can't seem to figure out the Permutation matrix. So I have summarised the process I am using let me know where it can be improved. Step 1: Using Gaussian Elimination with partial pivoting reduce A to form a...

Hi guys I have a question here relating integration by partial praction.. the question said what is the antiderivative of x^2+2x-1/2x^3 +3x^2 - 2x valid only when x > 1/2. anyway i had poor background in math and working hard to catch up... I don't understant why "valid only...

In partial fractions, why \frac{3x+5}{(1-2x)^2} = \frac{A}{(1-2x)^2} + \frac{B}{(1-2x)} and not \frac{3x+5}{(1-2x)^2} = \frac{A}{(1-2x)} + \frac{B}{(1-2x)} Why exists the exponent on the denominator in the right hand side of the equation?

Homework Statement Find functions y=y(x) defined on (-∞,0) or (0,+∞) which verify: xy'+(x2-1)cot(y)=0, y(x_0{})=y_0{} for x_0{}≠0 and cos(y_0{})≠0The Attempt at a Solution I'm really stuck on this one! Any help will be very much appreciated!

Homework Statement Hi. My first post! I'm trying to solve for where a is a constant: ∫ (x/a)1/2*(x/(x-a)) dx Homework Equations See above The Attempt at a Solution I've tried integration by parts by setting u=(x/a)1/2 but I end up having to solve ∫ (x/a)1/2ln(x-a) - which I...

For a function such as w=5xy/z How would you find the partial derivative of w with respect to y or z? I've tried using basic logarithmic differentiation, but can't arrive at the correct answer. For reference, the correct answer is wy=5*(xy/z/z)*ln(x)

1. In the Khan academy video I watched on partial derivatives, I understand absolutely everything except for the last 20 seconds which confused me. http://www.youtube.com/watch?v=1CMDS4-PKKQ Using the formula: Z = x² + xy + y² @z/@x = 2x +y x=0.2, y=0.3 2(.2) + .3 = .7 What...

Homework Statement (x,y) = x√(xy) The answer says: fx=3/2*√(xy) fy=(x√x) / (2√y) fxx= (3√y) / (4√x) fxy= (3√x) / (4√y) fyx =(3√x) / (4√y) fyy = -(x√x) / (4y√ I don't get from the beginning. shouldnt fx be equal to (3/2)x^2 * (x^3 * y)^-(3/2)?? When I do second derivative fxx from fx, it...

Homework Statement x^2-x-13/(x^2+7)(x-2) hello i am having trouble solving this problem.. could anyone please show me how to do this step by step? i know polynomial long division is required before it can be converted to partial fractions. I also know the answer is 2x+3/x^2+7 - 1/x-2...

Homework Statement I want to check the answer to this question. ⌠ 2 x dx / (x+1) (x+2) ⌡ 1 Homework Equations The Attempt at a Solution For partial fraction I got A= -1 and B = 2 My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3

Homework Statement F(x,y,z)=0 x=a(y,z) y=b(x,z) z=c(x,y) what does \frac{\partial c}{\partial x} \frac{\partial b}{\partial z} \frac{\partial a}{\partial y} equal. Homework Equations maybe you could tell me? The Attempt at a Solution i've spent hours and hours and pages...

Homework Statement Consider the following reaction: CH3OH(g) <-> CO(g)+2H2(g) Calculate ΔG for this reaction at 298 K under the following conditions: PCH3OH=0.895atm PCO=0.115atm PH2=0.200atm Homework Equations ΔG=-R*T*ln(K) where R is the gas constant 8.314 J/molK, T is 298 in...

Hi, I have the following PDE-S\frac{\partial\vartheta}{\partial\tau}+\frac{1}{2}\sigma^2\frac{X^2}{S}\frac{\partial^2\vartheta}{\partial\xi^{2}} + [\frac{S}{T} + (r-D)X]\frac{\partial\vartheta}{\partial\xi}I am asked to seek a solution of the form \vartheta=\alpha_1(\tau)\xi + \alpha_0(\tau)...

Homework Statement In one of the workings of a question I couldn't solve(from solution sheet) there was one step I couldn't understand. Homework Equations \frac{1}{x^2+x+1} = \frac{1-x}{1-x^3} The Attempt at a Solution Tried partial fractions(unfactorable denominator) and could'nt get it...

I have x=x(t) and y=y(t) and I'm working in polar co-ordinates so $$x=rcos{\theta}$$ and $$y=rsin{\theta}$$. I want to find ${\theta}'(t)$ so by the chain rule I want $${\theta}'(x)*x'(t)+{\theta}'(y)*y'(t)$$. I know $${\theta}=arctan(y/x)$$ but how do I partially differentiate theta w.r.t x and y?