Partial Definition and 1000 Threads

Homework Statement I'm taking a fluid mechanics class and I'm having an issue with acceleration and background knowledge. I know this is ridiculous, but I was hoping someone might be able to explain it for me. Homework Equations I definitely understand: ##a=\frac{d\vec{V}}{dt}## And I...

I always see the example f(x,y)={xy/(x2+y2) if (x,y) =/= (0,0) and 0 if (x,y)=(0,0)} given as the example of a function where the partial derivatives exist at the origin but are not continuous there. I have a difficult time wrapping my head around this and was hoping someone could...

Find the two first-order partial derivatives of z with respect to x and y when z = z(x, y) is defined implicitly by z*(e^xy+y)+z^3=1. I started by multiplying the brackets out to give; ze^xy + zy + z^3 - 1 = 0 i then differentiated each side implicitly and got; dz/dx = yze^xy and...

Homework Statement let u be a function of x and y.using x=rcosθ y=rsinθ,transform the following expressions in the terms of partial derivatives with respect to polar coordinates:(d^u/dx^2(double derivative of u with respect to x)+d^2u/dy^2(double derivative of u with respect to y)...

It's been awhile since I've taken a differential equations course, so I just could not wrap my head around this one. Homework Statement I was given a lot of variables but it boils down to a partial differential equation that looks like: pT/pt = A*p^2T/px^2 + B*f(x) I am not looking for...

Homework Statement If z=\frac{1}{x}[f(x-y)+g(x+y)], prove that \frac{\partial }{\partial x}(x^2\frac{\partial z}{\partial x})=x^2\frac{\partial^2 z}{\partial y^2} Homework Equations The Attempt at a Solution I don't know how I'm supposed to find the partial derivative of z with respect to...

Hi, Is there a difference between \int f(x,y(x)) dx And \int f(x,y(x)) \partial x ? If so, how is the total integral written in terms of partial integrals? Thanks for your help.

Homework Statement 1. What happens to D = fxxfyy - (fxy)2 at (0,0) for f(x,y) = 9x4 - 6x2y2 + y4? Classify the critical point at (0,0). 2. How about if f(x,y) = (y - x2)(y - x4) ? Homework Equations See above ^. The Attempt at a Solution 1. Okay, so after taking all the partial...

Homework Statement If f(x,y,z) = 0, then you can think of z as a function of x and y, or z(x,y). y can also be thought of as a function of x and z, or y(z,x) Therefore: dz= \frac{\partial z}{\partial x}dx + \frac{\partial z}{\partial y} dy and dy= \frac{\partial y}{\partial x}dx +...

I'm not sure how to solve this: du/dt = 3 \frac{d^{2}u}{dx^{2}} These are the conditions: u(0,t)= -1 u(pi,t)= 1 u(x,0) = -cos 7x Suggestion: I should use steady state solution to get a homogeneous initial condition. Starting with separtion of variables u(x,t) = G(x)H(t) And...

Homework Statement Taking k and ω to be constant, ∂z/∂θ and ∂z/∂ф in terms of x and t for the following function z = cos(kx-ωt), where θ=t2-x and ф = x2+t. Homework Equations The Attempt at a Solution I'm finding this difficult as t and x are not stated explicitly. I know how to...

Homework Statement Find all first and second partial derivatives of the following function: z = e^(-ET) where E and T are functions of z. I know how to do partial differentiation, but not when the variables are functions of z? I don't understand - is there some sort of implicit...

Homework Statement Calculate ∂f/∂x and ∂f/∂y for the following function: yf^2 + sin(xy) = f The Attempt at a Solution I understand basic partial differentiation, but I have no idea how to approach the f incorporation on both sides of the equation nor what you would explicitly call this...

Homework Statement \int\frac{8x^{2}+5x+8}{x^{3}-1} Homework Equations Because the denominator can be reduced to (x-1)(x^{2}+x+1), I set up the partial fractions to be \frac{A}{(x-1)} + \frac{Bx+C}{(x^{2}+x+1)} The Attempt at a Solution I've solved for A, B, and C, and now have...

I figured out the answer to this already, but I wanted help on the reasoning behind it: In order to work out the problem we're supposed to determine the partial pressure of phosgene by subtracting 0.497 atm worth from the initial pressure of 1.31 atm (determined by using the ideal gas...

From a fraction with infinite sum in denominator to partial fractions?? I am currently studying a course on Perturbation Methods and in particular an example considering the following integral \int_{0}^{\frac{\pi}{4}} \frac{d\theta}{\epsilon^2 + \sin^2 \theta}. There's a section of the...

Homework Statement The surface z=f(x,y)=√(9-2x2-y2) and the plane y=1 intersect in a curve. Find parametric equations for the tangent line at (√(2),1,2).Homework Equations Partial derivativesThe Attempt at a Solution Okay, so I'm just trying to work through an example in my textbook, so...

Homework Statement f'_x = kx_k, k = 1, 2, ..., n The Attempt at a Solution The partial should be f(sub)x(sub)k, as in, the partial derivative of f with respect to x_k. I wasn't sure how to represent that using TeX. I'm honestly at a complete loss here, because I'm not entirely sure what the...

Hi, I am trying to work out the atomic inversion of the Jaynes cummings model using the density matrix. At the moment i have a 2x2 matrix having used the Von neumann equation (technically in Wigner function in x and y). Each of my matrix elements are 1st order pde's describing the...

Hello all, This is a homework problem for my CHE345 class. Not sure what to do here, please at least let me know if I'm in the right ballpark. Homework Statement A student decomposes KCLO3 and collects 35.2 cm^3 of O2 over water at 23.0°C. The laboratory barometer reads 751 Torr. The...

Hi all. I've recently started working a lot on my background in math and physics, since this year I began a new masters program which is quite math/physics heavy and I don't have a formal background in either field. I will try to get active on this forum, since I've been luring for some time and...

Evaluate partial derivative. chain rule?? I would like to represent the term identified in the image as (term 1) in terms of those partial derviatives that are known. Unfortunatly I just can't seem to wrap my head around it at the moment. :bugeye: A prod in the right direction would be...

Homework Statement I have an expression for the partial derivative of u with respect to s, which is \frac{\partial\,u}{\partial\,s} = \frac{\partial\,u}{\partial\,x}x + \frac{\partial\,u}{\partial\,y}y How do I compute \frac{\partial^2u}{\partial\,s^2} from this?

One last question to Integrate x^2/(1+4•x^2). I would assume you would do long division but 4x^2 is bigger than x^2. so would you either pull out a 1/4 and it would be 1/4 ∫ x^2/(1/4+•x^2) dx or would the first term when doing long division be 1/4? or am I just totally wrong and you...

the probability of finding particle is a constant with time <ψ|\partialψ/\partial(t)> = -<\partialψ/\partial(t)|ψ> , the equation holds for all ψ so the time derivative operator is an anti-hermitian operator, but then consider any hermitian operator A, the rate of change of A is d(<ψ|Aψ>)/dt =...

Ok all save y'all a little reading. Worked out the problem. Got X^2+2x-1=A(2x-1)(x+2)+bx(x+2)+cx(2x-1) Ok then you write it standard form for a polynomial. Then use can use there coefficients to write new equations at you get 2a+b+c=1 3a+2b-c=2 and finally -2a=1 Now you solve for...

$x = r\cos\theta$ and $y=r\sin\theta$ $$ \frac{\partial u}{\partial\theta} = \frac{\partial u}{\partial x}\frac{\partial x}{\partial\theta} + \frac{\partial u}{\partial y}\frac{\partial y}{\partial\theta} = -r\sin\theta\frac{\partial u}{\partial x} + r\cos\theta\frac{\partial u}{\partial y} $$...

Homework Statement Consider an object that is coasting horizontally subject to a drag force f = -bv = cv^2. Write down Newton's second law... The Attempt at a Solution So I did all of the steps leading up to this: m∫\frac{dv}{bv+cv^2}=-t dt Using partial fractions I get \frac{1}{bv+cv} =...

Any help would be much appreciated - Is it possible to say the following? If z = g(s+at) + f(s-at), let u = s+at and v=s-at, where a is a constant. z = g(u) + f(v), \frac{∂z}{∂u} = g'(u), \frac{∂^{2}z}{∂v∂u} = 0? or can ∂u and ∂v not even exist because it depends on two variables (a and...

Use a geometric or algebraic argument to find a formula for the partial sums $A_n$ of an arithmetic sequence. I know that the partial sum is $S_n = n/2(2a_1+(n-1)d)$ where d is the difference. $A_n = \sum\limits_{k = 1}^n a_k$ I can come up with $n/2(a_1+a_n)$ but how do I get the difference?

Hi I am currently looking at some literature for the production of different radioactive nuclei under the bombardment of protons on Copper. I found something called partial γ-ray production cross-sections and I am wondering what this means. I know that cross-sections generally describe the...

I am working on some problems for an assignment in my PDEs class and find myself either not understanding what I am supposed to do or being unsure of my answers or the next step. I am going to outline my understanding of the problems, provide my attempt at a solution and highlight where I am...

Homework Statement ∇^{2}u=0 on 0<x<∏, 0<y<2∏ subject to u(0,y)=u(∏,y)=0 and u(x,0)=0, u(x,2∏)=1Homework Equations -- The Attempt at a Solution I've solved the SLP, and now I am trying to solve the Y-equation that results from separation of variables: Y''-λY=0, Y(0)=0...

Homework Statement determine the indefinite integral: ∫ (4x+10)/(9x^2+24x+16) dx Homework Equations partial fractions technique The Attempt at a Solution i know it's partial fractions and i thought i did it right but i got the wrong answer. (4x+10)/(9x^2+24x+16) =...

Homework Statement Prove that (∂P/∂V) n,T = 1/(∂V/∂P) n,T n and T are supposed to mean that theyre just constants Homework Equations Ideal Gas PV=nRT The Attempt at a Solution I tried (∂P/∂V) n,T= ∂nRT/v/∂V = ∂nRT/V ∂V then I am stuck here

Homework Statement Find ∫18/((x2+9)(x-3)) Homework Equations The Attempt at a Solution Im a little stuck on this. 18∫1/((x2+9)(x-3)) Im not sure how to turn this into a partial fraction.. help. Thanks

Homework Statement Please look at the attached pic. I don't know how to type all these symbols in. Homework Equations Im not sure how to start The Attempt at a Solution I tried using the cyclic rule but the problem just started getting messier.

Homework Statement Parametrize the upper half of the unit circle by x = cos(t), y = sin(t), for 0\leq t \leq\pi Let T = f(x,y) be the temperature at the point (x,y) on the upper half of the circle. Suppose that: \frac{\partial T}{\partial x} = 4x - 2y \frac{\partial T}{\partial y} = -2x +...

For PFE, can a denominator variables with coefficient of something other than 1, or does it have to be 1? For Example, can I have a term A/(3x+9)? It's been years since I've dealt with this and don't quite remember if this was a rule or not. Thanks! EDIT: This is in terms of taking the...

Homework Statement I need to integrate v(t) = V( \frac{1- e^{-2gt/V}}{1+ e^{-2gt/V}}) to show that the position function is given by s(t) = Vt + \frac{V^2}{g}ln(\frac{1 + e^{-2gt/V}}{2}) Homework Equations g is the acceleration due to gravity V is the terminal velocity The Attempt at...

find the valu of local extremum for f(x)=sin x-cos x,0<x<2∏.

Im reading Lang's first course in calculus and can't understand one step that he does when trying to integrate quotients with quadratic factors in the denominator. He's trying to find the integral of \int{\frac{1}{(x^2+1)^n}dx} but he's first starting with the case where n=1 Then while...

say you have a function f(x,y) \nablaf= \partialf/\partialx + \partialf/\partialy however when y is a function of x the situation is more complicated first off \partialf/\partialx = \partialf/\partialx +(\partialf/\partialy) (\partialy/\partialx) ( i wrote partial of y to x in case y was...

Homework Statement \int\frac{1}{x\sqrt[3]{x+1}}dx (That's a cubic root in the denominator, by the way. Not an x cubed.) The Attempt at a Solution I thought possibly partial fractions, but I've never seen it done with a root in the denominator. Integration by parts was...

hello, I've spent a good couple hours diving back into the world of differential equations after being out of the game for a good 2 years. I started getting a hang of solving them till i came across this problem: Solve the following differential equation with the 3 given cases, all of the...

Find the first order partial derivatives of the function x = f(x,y) at the point (4,3) where: f(x,y)=ln|(x+√(x^2+y^2))/(x-√(x^2+y^2))| I understand the method of partial derivatives and implementing the given point values once the partial derivatives are found, however I am having trouble...

Homework Statement The problem is attached in the picture. The Attempt at a Solution I'm aware that: dU = T dS - P dV ∫ dU = ∫ (T) dS - ∫ P dV Are they assuming that T, P are constant so U = TS - PV ∂U/∂X = T (∂S/∂X) - P (∂V/∂X) Or is there a way to directly...

Partial Pressure Help---Please Check The Partial Pressure of water vapor at T = 273 K is 6.11 mbar. Find the corresponding mass concentration of water vapor. Assume P = 1 atm. So... ρH20 = (PH20*MH20/(R*T) ρH20= (6.11*10^2 Pa)*(18.01 g/mol)/(8.314*273 K) ρH20 = 11004.11/2269.722 =...

Folks, I am stuck on an example which is partial differenting a functional with indicial notation The functional ##\displaystyle I(c_1,c_2,...c_N)=\frac{1}{2} \int_0^1 \left [ \left (\sum\limits_{j=1}^N c_j \frac{d \phi_j}{dx}\right )^2-\left(\sum\limits_{j=1}^N c_j \phi_j\right)^2+2x^2...

hello world, I've been doing some summertime training to brush up my math skills and have been struggling with this [dy]/[/dt]=(4exp(-y)+const*exp(-2y))^1/2 In fact this is the simplified version of a Bernouilli equation. I know that it is separable, I'm just struggling with the...