Partial Definition and 1000 Threads

Homework Statement \frac{x}{(x+4)^{2}} Homework Equations The Attempt at a Solution I make the integrand equal to the following: \frac{A}{(x+4)}+\frac{Bx+C}{(x+4)^{2}} Then after finding a common denominator I get x = A(x+4)^{2}+(Bx+C)(x+4) But that cannot be...

Homework Statement Utt-Uxx+2Uxy-Uyy=0 with the conditions: U(1,x,y)=cos(x)+ey Ut(1,x,y)=sin(x)-y2 Homework Equations Not using separation of variables to solve. The Attempt at a Solution I've gotten the general equation to be of the form: U(t,x,y)=ψ(x+t,y-t)+ζ(x-t,y+t)...

Homework Statement A scalar field is given by the function: ∅ = 3x2y + 4y2 a) Find del ∅ at the point (3,5) b) Find the component of del ∅ that makes a -60o angle with the axis at the point (3,5) Homework Equations del ∅ = d∅/dx + d∅/dy The Attempt at a Solution I completed part a: del ∅ =...

I have this partial differential equation that I have to solve, and I thought that perhaps there was an easy way of solving this, like finding an equivalent differential for the right hand side of the equation, on such a way that I could get a simple differential equation, and then just...

Homework Statement I want to show that the partials exist for a certain function. Homework Equations My book says that if a function f is differentiable at a point x then the partial derivatives exist. The Attempt at a Solution Rather than showing f is differentiable, I am...

Hi there. I have this partial differential equation that I have to solve, and I thought that perhaps there was an easy way of solving this, like finding an equivalent differential for the right hand side of the equation, on such a way that I could get a simple differential equation, and then...

I just want to know if there is now a way to solve fractions like which had a variables that has a degree more than 2 in its denominator. I know that denominators having degrees of 2 could be solved using (Ax + B)/(x2+a). But how about denominators like (x3+a) and so on?

In this textbook, how exactly are 2.2.19 and 2.3.21 equal? http://i.imgur.com/LrcXE.png

Hello all, Say one wants to find the inverse Laplace Transform of a function, and the method for attaining the solution is executed via partial fractions. Do the real numbers go with the complex numbers when determining the constants of partials? Perhaps this is wordy. I'll provide a theoretical...

Homework Statement Rewrite this in terms of f, f, ∂f/∂x, and x: ∂f(x,y)/∂(%Δx) = ∂f(x,y)/∂(d log(x) ) Homework Equations ∂(%Δf(x,y))/∂(%Δx) = ∂logf(x,y)/∂log(x)= ∂f(x,y)/∂x*x/f(x,y). ∂f(x,y)/∂log(x)=x∂f(x,y)/∂x The Attempt at a Solution I found that (%Δx) can be written as...

Hello everyone, I'm trying to understand more about how partial pressure works and how to use chemical activity equation. My reference text uses the following example: Note1: A solution is prepared by mixing 2 moles of CHCl3 (chloroform) and 3 moles of (C2H5)2O (diethyl ether). Note2: The...

let f(x, y') = x + y' where y' = dy/dx then is it true, and why, that the partial derivative of f with respect to y' = 1 in this case we consder dx/dy' = 0, as if they are independent of each other.

Given a function z(x,y), is the following expression valid: ∫(1)∂z = z Does this even make sense? I came up with this in my differential equations class, but I'm not sure if it actually means anything.

Homework Statement A gas mixture of 0.13 mol NH3, 1.27 mol N2, and 0.025 mol H2O vapor is contained at a total pressure of 830 mm Hg and 323 K. Calculate the following: (a) Mole fraction of each component. (b) Partial pressure of each component in mm Hg. (c) Total volume of mixture in m3...

Homework Statement A question in a book has partially differentiated a function f(x,y) = x^2 + 8xy^2 + 2y^2 df/dx = 2x + 8y^2 = 0 at stationary point (eqn 1) df/dy = 16xy + 4y = 0 at stationary point (eqn 2) Homework Equations The Attempt at a Solution It then states...

partial orders :hasse diagrams theorem : if [A,R] is poset and A is finite , then A has both a maximal and a minimal element A={a1,a2,a3...an} but i know prove it is maximal , but i not know how i prove it is minimal ? please answer ?

Hi, I remember having read in basic calculus that the following is true, but I don't know what this property is called and am having a hard time finding a reference to this. d u(x,y) = \frac{\partial u}{\partial x} dx + \frac{\partial u}{\partial y} dy Ques: Is this true ? Is this true for...

Homework Statement Hi I need some help in proving that \partial^2 V / \partial x^2 + \partial^2 V / \partial y^2 = 0 , when V = 1/2ln(x^2+y^2) Homework Equations The Attempt at a Solution For \partial V / \partial x here's what I get: (1/x^2+y^2) *2x*1/2 = x * (x^2+y^2)^-1 and for \partial V...

[b]1. I am asked to write a procedure that will inverse square matices using LU factorization with partial pivoting. [b]2. I am also told that the procedure should return the inverse matrix and report an error if it cannot do so. [b]3. So far I've come up with the code below but...

Homework Statement Here is the problem: Carbon monoxide and oxygen are kept at exactly 300 K in separate chambers of the apparatus shown below. When the stopcock is opened, the combustion reaction begins and is allowed to proceed to completion, while being maintained at exactly 300 K...

I was working two different but superficially related problems, and noticed that if I did something that is generally not allowed, the results were connected by a negative sign. My questions are whether this will always turn out this way, and if so, why. The two problems were (A)...

Hello all! :smile: I have searched this, but I am still looking for additional input. I am an engineer and I want to self-study PDEs. I looked at Farlow's text and though it is nice from an applications standpoint, I think that it is not 'mathy' enough for me. Don't get me wrong, I am not the...

Homework Statement Can partial reflection-partial refraction occur with all waves (ie. other than light)? Homework Equations The Attempt at a Solution My textbook constantly refers to light and apparently so does Google. "For still larger incident angles there is no...

I know that for any C2 function, the mixed second-order partials are equal, and I see that this should extend inductively to a statement about the kth partials of a Ck function, but I am having trouble figuring out exactly how this works. For example, take f:ℝ2 → ℝ . fxxy=fxyy is not true...

Homework Statement Consider the following system of (first order) differential equations: \dot{x}=f(t_1,x,y,z) \dot{y}=g(t_2,x,y,z) \dot{z}=h(t_3,x,y,z) where \dot{x}=\frac{\partial x}{\partial t_1}, \dot{y}=\frac{\partial y}{\partial t_2}, and \dot{z}=\frac{\partial z}{\partial...

Hello! I was wondering how I could find the following derivatives from the given function using Jacobian determinants. f(u,v) = 0 u = lx + my + nz v = x^{2} + y^{2} + z^{2} \frac{∂z}{∂x} = ? (I believe y is constant, but the problem does not specify) \frac{∂z}{∂y} = ? (I...

Given some natural number n find the nth partial sum for: \displaystyle\sum_{k=0}^{\lfloor log(n) \rfloor} \lfloor \frac{n}{10^k} \rfloor I find this question really difficult! If anyone could help, it would be greatly appreciated. Thanks in advance!

Given that the Van Der Waals equation is (p + (an^2)/v^2)(v-nb)=nRT where n,a,R and b are constants... How to we find the derivative of p wrt v ? How to find the derivative of p wrt T without further differentiation ?? Can anyone teach me how to do this question ? Sincerly thanks~

Hi there, just wanted to make a clarification before my final exam. The second derivative test for partial derivatives (or at least part of it) states if D = ∂2f/∂x2 * ∂2f/∂y2 - (∂2f/∂x∂y)2 and (a,b) is a critical point of f, then a) if D(a,b) > 0 and ∂2f/∂x2 < 0, then there is a local...

Homework Statement The question asks: f(x,y) = 3xy+5y^3/[x^2+y^2] when (x,y) =! (0,0) f(x,y) = 0 when (x,y) = (0,0) what is df/dy at (0,0)? Homework Equations The Attempt at a Solution I'm not sure what the answer is. At 0,0 f(x,y) is 0, so it's simply a point and the...

So I'm trying to figure out how to find that partial sum of a given summation of a series on maple 13. Iv tried looking all over the internet for answers to my problem, but no site seems to answer my problem. I am trying to find the sum of a series. When i plug in 1/x^2 and evaluate I get the...

Methane from natural gas could be a great source of energy (eg. in thermoelectric plants), but the need to curb CO2 emissions stands in the way. I wonder whether one could get useful energy from some partial combustion reaction of CH4, that yields H2O plus some carbon-containing solid that...

Hi, I would like to confirm that I have understood this correctly. The steps to find local maxima/minima of a function f(x1, ... , xn) are: 1) We find all the stationary points. 2) We form the Hessian matrix and calculate the determinants D1, D2... Dn for a stationary point P we want to check...

Homework Statement Given that the surface (x**5)(y**2)+(y**5)(z**3)+(z**3)(x**2)+4xyz=7 has the equation z=f(x,y) in a neighbourhood of the point (1,1,1) with f(x,y) differentiable, find the derivatives (∂**2f)/(∂x**2) at (1,1) Homework Equations The Attempt at a Solution I...

I am a little confused as to notation for convergence. I included a picture too. If you take a look it says "then the series Ʃan is divergent" Does the "Ʃan" just mean the convergence as to the sum of the series, or the lim an as n→ ∞ nth term? I believe it is the sum of the series but I...

At my school, Physics majors are the only ones who HAVE to take PDE, math majors and engineers have the option as an elective, but none of them do that because it has the reputation of being the most difficult math course at my school. I'm going into Calc III in the spring, then DE is next...

Is it possible to find a non-recursive formula for the partial sums of a convergent series?

I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by: dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant) v(t = 0) = C (constant value) v(x = 0) = 0 I'm not quite sure how to solve this. I was thinking about using the method of...

Homework Statement This is from a physics problem, but says to evaluate the other three terms in the equation. Going to just show the first one. Homework Equations (\theta 1/sin\theta d/d\phi)(\phi d/d\theta) The Attempt at a Solution in the book they show the solution, but no...

when we fill a container with water so as to leave some space above the surface of water. And we close the container. When we turn the tube upside down. The air which which was above the surface of water transfers to the other side. How does this happen. Does air penetrate water? And suppose...

Homework Statement So using standard spherical polar co-ordinates, my notes define a sphere as r(s,t) = aCos(s)Sin(t) i + aSin(s)Sin(t) j + aCos(t) k and the normal to the surface is given by the cross product of the two partial differentials: \partialr/\partials X \partialr/dt...

Homework Statement The activity coefficient of zinc in liquid brass is given (in joules) by the following equation for temperatures 1000-1500 K: RT ln γZn = -38,300 x2Cu where xCu is the mole fraction of copper. Calculate the partial pressure of pure zinc PZn over a solution of 60 mol%...

Homework Statement The PDE: {\partial \rho \over \partial t} + \rho {\partial \rho \over \partial x} =-x\rho and \rho(x,0) = f(x) Determine a parametric representation of the solution. Homework Equations {dx\over dt} = \rho {d\rho \over dt} = -x\rho The Attempt at a Solution Using method of...

Homework Statement Are these two relations reflexive, antisymmetric, transitive? 1. (w,x)<=(y,z) iff w+x <= y+z 2. (w,x)<=(y,z) iff w+x <= y+z AND w<y Homework Equations The Attempt at a Solution 1. reflexive - yes; antisymmetric - no; transitive - yes; 2. reflexive -...

Homework Statement Find (x,y) which maximizes f(x,y) for x ≥ 0. f(x,y) = e-x - e-2x + (1 - e-x)(4/5 - (3/4 - y)2)Homework Equations The Attempt at a Solution Due to the question prior to this one, I know all the first order and second order partial derivatives of the formula. I do not...

Homework Statement When two resistors R1 and R2 are connected in parallel, their effective resistance R = (R1R2)/(R1+R2). Show that is R1 and R2 are both increased by a small percentage c, then the percentage increase of R is also c. Homework Equations The Attempt at a Solution I...

Homework Statement Use partial fractions to rewrite: (2z)/(z^2+3) Homework Equations noneThe Attempt at a Solution I did this: (2z)/(z^2+3) = (Az+B)/(z^2+3) 2z = Az +B A = 2, B = 0...problem is that it just recreates the original Here is their example in the book: 1/(z^2+1) =...

a) Determine K at 298K for the reaction H2(g) + Cl2(g) <---> 2HCl(g) b) The equilibrium partial pressure of HCl is 1 bar. Determine the equilibrium partial pressures of H2 and Cl2. This question was on my test. I got K= 3.2 x 10^-34 using dG*=-RTlnK when dG=0 at equilibrium. I'm having...

If z = f(x,y) and x = e^{u}, y =e^{v} Prove: x^{2}\frac{\partial^{2}z}{\partial x^{2}} + y^{2}\frac{\partial^{2}z}{\partial y^{2}} + x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = \frac{\partial^{2}z}{\partial u^{2}} + \frac{\partial^{2}z}{\partial v^{2}} I used u...

Basically I have a question (2nd Screenshot) which I am trying to mirror with the below example, which has a written solution. What I can't work out is how the solutions would differ given the boundary conditions, where would I put them in? Are the soutions to both problems the same? Here...