Partial Definition and 1000 Threads

How is the double derivative equal to that in the equation 2 in the attachment? =|

I am utilitizing rotation vectors (or SORA rotations if you care to call them that) as a means of splitting 3D rotations into three scalar orthogonal variables which are impervious to gimbal lock. (see SO(3)) These variables are exposed to a least-squares optimization algorithm which...

Here is the question: Here is a link to the question: Help with Calculus BC: partial fractions!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

In a thermodynamics question, I was recently perplexed slightly by some partial derivative questions, both on notation and on physical meaning. I believe my questions are best posed as examples. Suppose we have an equation, (\frac{\partial x(t)}{\partial t}) = \frac{1}{y}, where y is a...

Homework Statement Suppose c_{n} > 0 for each n\geq 0. Prove that if \sum ^{\infty}_{n=0} c_{n} is Cesaro summable, then the partial sums S_{N} are bounded. Homework Equations -- The Attempt at a Solution I tried contraposition; that was getting me nowhere. I have a few...

1. So, i have the next integrand... 2. \int \frac{1}{(x-1)^2(x+1)^2}\,dx 3. I proceeded by resolving it by partial fraction and i came up with the next... \int \frac{1}{((x-1)^2)((x+1)^2)}\,dx = \int \frac{A}{(x-1)} + \frac{B}{(x-1)^2} + \frac{C}{(x+1)} + \frac{D}{(x+1)^2}\,dx The thing is...

Homework Statement Use the method of partial fractions to show that: $$\frac{2x^2}{(1-x(1+x)} $$ , may be written as: $$-2+\frac{1}{1-x}+\frac{1}{1+x}$$ , where $$\lvert x\rvert\neq1 $$. Homework Equations The Attempt at a Solution I obviously know how to do it but in the...

Author: David Bleecker (Author), George Csordas (Author) Title: Basic Partial Differential Equations Amazon Link: https://www.amazon.com/dp/1571460365/?tag=pfamazon01-20 Prerequisities: Table of Contents: Preface Review and Introduction A Review of Ordinary Differential Equations...

Homework Statement compute the gradient: ln(z / (sqrt(x^2-y^2)) Homework Equations ∇=(∂/(∂x)) + ... for y and z I just want to know how to do the first term with respect to x The Attempt at a Solution I am so rusty I don't know where to begin.

Homework Statement The function f(x,y,z) may be expressed in new coordinates as g(u,v,w). Prove this general result: The Attempt at a Solution df = (∂f/∂x)dx + (∂f/∂y)dy + (∂f/∂z)dz dg = (∂g/∂u)du + (∂g/∂v)dv + (∂g/∂w)dw df = dg since they are the same thing? but the...

I've been trying to get out this question for a while now: ai) Show that (x,y,z) = (1,1,1) is a solution to the following system of equations: x + y + z = 3 2x + 2y + 2z = 6 3x + 3y +3z = 9 aii) Hence find the general solution of the system b) Express 2x^2 + 3/(x^2 + 1)^2 in partial...

Plese give me silminer simple example or anther example on this case or explein the steps

I have the following equation \frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0 where y is a function of x and m is a function of y. If I integrate this equation first with respect to y should I get a function of x as the constant of integration (say C\left(x\right)) or it is just...

let f = x2 + 2y2 and x = rcos(\theta), y = rsin(\theta) . i have \frac{\partial f}{\partial y} (while holding x constant) = 4y . and \frac{\partial f}{\partial y} (while holding r constant) = 2y . i found these partial derivatives by expressing f in terms of only x and y, and then in...

Homework Statement x3 + y3 + z3 - 3xyz = 6 Find (∂y/∂x)z. Homework Equations [b]3. The Attempt at a Solution [/ can i simply take the partial derivative of both sides treating z as constant? x3 + y3 + z3 - 3xyz - 6 = 0 f(x,y,z) = 0 (∂f/∂x)z = 0

Hi everyone, I am working on simplifying a differential equation, and I am trying to figure out if a simplification is valid. Specifically, I'm trying to determine if: \frac{\del^2 p(x)}{\del p(x) \del x} = \frac{\del^2 p(x)}{\del x \del p(x)} where p(x) is a function of x. Both p(x)...

Homework Statement Given that u(x,y) and y(x,z) are both continuous, differentiable functions show that (\frac{\partial u}{\partial z})x=(\frac{\partial u}{\partial y})x(\frac{\partial y}{\partial z})x Homework Equations Only equations given above The Attempt at a Solution I...

Homework Statement Determine whether a function with partial derivatives f_x(x,y)=x+4y and f_y(x+y)=3x-y exist. The Attempt at a Solution The method I've seen is to integrate f_x with respect to x, differentiate with respect to y, set it equal to the given f_y and show that it can't be...

I'm working on a calculus project and I can't seem to work through this next part... I need to substitute equation (2) into equation (1): (1): r\frac{\partial}{\partial r}(r\frac{\partial T}{\partial r})+\frac{\partial ^{2}T}{\partial\Theta^{2}}=0 (2): \frac{T-T_{0}}{T_{0}}=A_{0}+\sum from n=1...

I have an electrostatics problem (shown here: https://www.physicsforums.com/showthread.php?t=654877) which leads to the following system of differential equations: \frac{\partial E_z}{\partial z}=\frac{\rho}{\epsilon_0} (1) Z_i E_r \frac{\partial \rho}{\partial r}+(u_g+ Z_i E_z)...

Hi guys, attached is a picture of my problem and it is also underlined. I've been reading through this theory and I just don't understand what the square brackets indicate. I understand that ∇phi is the partial derivative with respect to the scalar function phi. But what is ∇phi...

Homework Statement Given the initial value problem: \frac{(u)}{(1-e^-(2x))}u_{x}+ \frac{\sqrt{t}}{u}u_{t}=1, with x, t, u > 0 Subject to condition u(x,1)=e^{-x} Homework Equations a) Classify given partial differential equation. b) Write the characteristic equations. By...

Homework Statement How to get partial fraction decomposition for \frac{1}{(x^2+a^2)(x^2+p^2)}Homework Equations The Attempt at a Solution I tried with \frac{1}{(x+ia)(x-ia)(x+ip)(x-ip)}=\frac{A}{x+ia}+\frac{B}{x-ia}+\frac{C}{x-ip}+\frac{D}{x+ip} and get the result at the end of the day. Is...

Homework Statement At 100 o C Kc=.078 for the reaction SO2Cl2<-->SO2 + Cl2. In an equilibrium mixture the [SO2CL2]=.0108 M and [SO2]=.052 M. What is the partial pressure of Cl2 in the eq. mixture? Homework Equations Kp=Kc(RT)\Deltan P=RT/V The Attempt at a Solution I solve for...

I have a question to ask, is dx = δx, can they cancel each other like \frac{dx}{δx}=1 and is it mean that: \frac{δf}{δx}\frac{dx}{dt}=\frac{df}{dt}? (f = f (x,y,z))

Homework Statement Consider the following equality: (\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V If I rearrange the equality so that I write: (\frac{∂S}{∂P})? = (\frac{∂V}{∂T})? What variables will be constant in each side? I'm having some trouble in a few thermodynamics problems because...

Homework Statement Consider the following equality: (\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V If I rearrange the equality so that I write: (\frac{∂S}{∂P})? = (\frac{∂V}{∂T})? What variables will be constant in each side? I'm having some trouble in a few thermodynamics problems because...

Suppose I have a transformation (x'_1,x'_2)=(f(x_1,x_2), g(x_1,x_2)) and I wish to find \partial x'_1\over \partial x'_2 how do I do it? If it is difficult to find a general expression for this, what if we suppose f,g are simply linear combinations of x_1,x_2 so something like ax_1+bx_2 where...

Homework Statement Prove that if ##z=\arctan(\frac{xy}{\sqrt(1+x^2+y^2)})## , then: ##\frac{\partial^2 z}{\partial x \partial y}=\frac{1}{(1+x^2+y^2)^\frac{3}{2}} ## Homework Equations ##\frac{d}{d x} (\arctan(x)) = \frac{1}{1+x^2}## The Attempt at a Solution Differentiating z...

Homework Statement f(x,y) = y^2 + (x^3)*sin(1/x) when x =/= 0 = y^2 when x = 0 i want to prove fx(x,y) is not continuous at (0,0) Homework Equations The Attempt at a Solution i found when x=/=0 , fx = 3(x^2)sin(1/x) - xcos(1/x) -----eq(1)...

Could someone please explain how the formula at the bottom of the page is derived i.e. how is the Taylor theorem used to obtain it ?

Homework Statement I have this series 1^{3}-2^{3}+3^{3}-4^{3}+5^{3}-6^{3} + \ldots Homework Equations and sequence of partial sums for this series that is: S_n = \sum_{k=0}^{n}(-1)^{k+1} k^3 = \dfrac{1 + (-1)^n(4n^3 + 6n^2-1)}8 =\begin{cases} \dfrac{2n^3+3n^2}4; & n \text{ is...

partial differential = the change?? Homework Statement How is Δy/Δx = \partial y / \partial x ? I just don't know the logic behind this.

Homework Statement I'm trying to understand how a certain substitution can be made with regards to taking the partial derivative of a function product when the variable I am differentiating by is a function itself.Homework Equations (∂/∂p) (v(p)p(x,t)) = v(p) + (∂v/∂p)pThe Attempt at a...

Just curious if anyone has any good recommendations for books or resources on Linear Partial Differential Equations. Thanks.

Homework Statement Suppose I have two substances in a solution, each forming an equilibrium with its corresponding vapor phase, and thus having its own partial pressure. How can I measure this partial pressure of one of the components, given the pressure of each component in its pure form...

U is internal energy T is temperature v is volume U(T,v) My book say (∂u/∂v) at constant temperature can be calculated from the equation of state. How to calculate it? Thank you

Whoa, this here is kicking me hard! Okay, so I've got everything pretty well down until... stuff like... \int \frac{3x + 32}{x^{2}-16x + 64}dx So, I get how to factor the denominator, but then what? The above won't factor... Also, I read that if the degree of the numerator is higher than the...

We have an empty vessel with volume of 2L. We put 2.42gr of PCl5 (g) and allowed it to partially decompose at 250 Celsius according to: PCl5 --> PCl3 + Cl2 the two prodcuts are also gases. The total pressure inside the vessel after this partial decomposment is 359 torr. What is the partial...

Homework Statement Suppose f: R^2 --> R is differentiable and (df/dt) = c(df/dx) for some nonzero constant c. Prove that f(x, t) = h(x + ct) for some function h. Homework Equations hint: use (u, v) = (x, x+ct) The Attempt at a Solution df/dt = limk-->0 (f(x, x+ct+k) - f(x...

Homework Statement Suppose f: R -> R is differentiable and let h(x,y) = f(√(x^2 + y^2)) for x ≠ 0. Letting r = √(x^2 + y^2), show that: x(dh/dx) + y(dh/dy) = rf'(r) Homework Equations The Attempt at a Solution I have begun by showing that rf'(r) = sqrt(x^2 + y^2) *...

what does d/ds (e^s cos(t)du/dx + e^s sin(t)du/dy) give, given that u = f(x,y) i don't know how to manipulate d/ds and how to derive using d/ds. i am trying to simplify the expression, but i don't know, i just get stuck in the middle of can't get farther than here...

Homework Statement If u=f(x,y) where x=escost and y=essint show that d2u/dx2+d2u/dy2 = e-2s[d2u/ds2+d2u/dt2 Homework Equations http://s11.postimage.org/sjwt1wkvl/Untitled.jpg The Attempt at a Solution ok i don't understand how they got to that i don't know what d/ds is...

I have a question but have not seen an example or find anything in my textbooks so would love some advice on how to understand the problem. Its a theory question on partial derivatives of the second order... T=T(x,y,z,t) with x=x(t), y=y(t), z=z(t). Find the second derivative of T wrt t So...

Homework Statement ∫ (x^3)/(x^2+2x+1) I think I could solve it if I knew how they did this operation: From the solution: ' (x^3)/(x^2+2x+1) = (x-2) + (3x+2)/(x+1)^2 ( After long division) Did they use polynomialdivision? x^3: x^2-2X+1= If so, how?

Hi, Trying to find all partial limits of cos(pi*n/3), I separated it into: a_3k -> -1 a_6k -> 1 Is this a valid approach? Are there any other partial limits?

Homework Statement Hi I just have a problem in regards to setting up your partial fractions when doing nonhomogeneous differential equations using Laplace transforms. I’m at the stage of getting the inverse Laplace of: (1-625S^4)/(S^3 (25S^2+1) ) Homework Equations The Attempt...

Homework Statement The steady state temperature distribution T(x,y) in a flat metal sheet obeys the partial differential equation: \displaystyle \frac{\partial^2 T}{\partial x^2}+ \frac{\partial^2 T}{\partial y^2} = 0 Seperate the variables in this equation just like in the...

Meaning of "in partial fulfillment" In a thesis one often finds this sentence: "A thesis submitted in partial fulfillment of the requirements for the degree of... ", e.g. here: http://dmg.caup.washington.edu/pdfs/Thesis.HunterRuthrauff.2012.pdf What does "in partial fulfillment" mean, in...

So far I have only seen ∂/(∂y) as being interpreted as an operator being of no use unless it is applied to some vector etc. Now, however, my course literature asserts the following equality: y=∂/(∂y) What is the interpretation of the differentials in this case?