Partial Definition and 1000 Threads

Hi everyone. Some years ago I read about the Crower six cycle engine. Always wanted to understand it better. And now is the time to follow up on that desire. I’m trying to calculate what happens during the water injection. The goal is to determine the conditions (pressure, temperature)...

Homework Statement Find the partial fraction decomposition for: ##\frac{1}{\left(x^2-1\right)^2}## Homework EquationsThe Attempt at a Solution Please see my attached images. I think the image shows my thought process better and it would take me well over an hour to type all that out! Im...

There is a problem in a PreCalculus book that I'm going over that states: Express the sum ##\frac{1}{2⋅3}+\frac{1}{3⋅4}+\frac{1}{4⋅5}+...+\frac{1}{2019⋅2020}## as a fraction of whole numbers in lowest terms. It goes on to state that each term in the sum is of the form...

Hi, I'm attempting to learn differential equations on my own. Does anyone recommended a textbook that comes with/has a solution manual? I learn faster when I can see a problem worked out if I can't solve it. Thanks.

Homework Statement Hello I am given the equation: ut - 2uxx = u I was given other equations (boundary, eigenvalue equations) but i don't think I need that to solve this first part: The book says to get rid of the zeroth order term by substituting u = exp(t)V(x,t). I tried to but I can't find...

In Section 7.6 - Equivalence of Lagrange's and Newton's Equations in the Classical Dynamics of Particles and Systems book by Thornton and Marion, pages 255 and 256, introduces the following transformation from the xi-coordinates to the generalized coordinates qj in Equation (7.99): My...

Does anyone know a rigorous proof for Dalton's law ? I think I saw it once, but I can not find it again anywhere. Thanks Ric

I have seen how to solve the heat equation: $$ \frac{ \partial^2 u(x,t) }{\partial x^2} = k^2 \frac{ \partial u(x,t) }{\partial t} $$ With boundary conditions. I use separation variables to find the result, but i don't know how to solve the equation plus a...

1. The problem statement, all variables, and given/known data Given is a second order partial differential equation $$u_{xx} + 2u_{xy} + u_{yy}=0$$ which should be solved with change of variables, namely ##t = x## and ##z = x-y##. Homework Equations Chain rule $$\frac{dz}{dx} = \frac{dz}{dy}...

<Moderator's note: Moved from a technical forum and thus no template.> Hi everyone, I have encountered a partial differential equation with square roots which I don't have a clue in solving it. After letting z=F(x)+G(y), I can't really figure out the next step. I tried squaring both sides but...

1. The problem statement, all variables, and given/known data Task requires you to solve a partial differential equation $$u_{xy}=2yu_x$$ for ##u(x,y)##. A hint is given that a partial differential equation can be solved in terms of ordinary differential equations. According to the solution...

Hello MHB! (Wave) A young man in high school I know has been essentially tasked with finding the following partial sum: S=\sum_{k=0}^{n}\left(\frac{2^k}{3^{2^k}+1}\right) I honestly have no idea how to proceed, and I am hoping someone here can provide some insight. (Star)

Homework Statement y(w)= 3/(iw-1)^2(-4+iw) Homework Equations N/A The Attempt at a Solution 3/(iw-1)^2(-4+iw) = A/iw-1 + B/(iw-1)^2 + C/-4+iw for B iw = 1 B=3/-4+1 = -1 for C iw = 4 C= 3/(4-1)^2 = 1/3 I know the answer for A should be -1/3 however I am unsure how to obtain this as if the...

So, I'm now studying thermodynamics and our teacher proved some time ago the following mathematical result: If f(x,y,z)=0, then (∂x/∂y)z=1/(∂y/∂x)z But today he used this relation for a function of four variables. Does this result still hold, because I'm not really sure how to prove it. If...

Homework Statement Given $$L = \left(\nabla\phi + \dot{\textbf{A}}\right)^2 ,$$ how do you calculate $$\frac{\partial}{\partial x}\left(\frac{\partial L}{\partial(\partial\phi / \partial x)}\right)?$$ Homework Equations By summing over the x, y, and z derivatives, the answer is supposed to...

Hello everyone, I am trying to solve this wee problem regarding partial derivatives, and not sure how to do so. The following image shows level curves of some function \[z=f(x,y)\] : I need to determine whether the following partial derivatives are positive or negative at the point P...

im a bit confused about partial fractions If we have something like x/((x+1)(x+2)) we could decompose it into a/(x+1) +b/(x+2) If we had something like x/(x+1)^2 we could decompose it into a/(x+1) + b/(x+1)^2 We use a different procedure when there is a square in part of the polynomial in...

It seems that a partial solar eclipse is one in which the eclipse circle never completely rises, and it essentially is only a sunrise or sunset eclipse, with the point at which it goes from sunrise to sunset being that location in the polar region where the eclipse is at "high noon" but which it...

Why we write differently d in partial derivation differentiation? Is it because of several variables? Edited by mentor -- the action of finding a derivative is called differentiation.

Can total lunar eclipse and partial lunar eclipse be happened at the same time? So, do we call it partial lunar eclipse when the total lunar eclipse happen just before?

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of D&K's notation for directional and partial derivatives ... ... D&K's definition of directional and...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of D&K's notation for directional and partial derivatives ... ... D&K's definition of directional and...

Hi PF According to IEC 60885-2 and IEC 60270 the acceptance criteria in partial discharge (PD) measurements on high voltage cable insulation state that PD level should be below (< 5 pC). The insulation material that is refereed to is often XLPE which is a sensitive insulation to PD. Other...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with another aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with another aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read as...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of the proof of Proposition 2.3.2 ... ... Duistermaat and Kolk's Proposition 2.3.2 and its proof read as...

Existence of Partial Derivatives and Continuity ... Kantorovitz's Proposition pages 61-62 ... I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with another element of the proof of Kantorovitz's...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with another element of the proof of Kantorovitz's Proposition on pages 61-62 ... Kantorovitz's Proposition on pages 61-62 reads as follows: In the...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an element of the proof of Kantorovitz's Proposition on pages 61-62 ... Kantorovitz's Proposition on pages 61-62 reads as follows: I am...

I am reading the book "Several Real Variables" by Shmuel Kantorovitz ... ... I am currently focused on Chapter 2: Derivation ... ... I need help with an element of the proof of Kantorovitz's Proposition on pages 61-62 ... Kantorovitz's Proposition on pages 61-62 reads as...

- check if right check if right Now, 2 seems to be the right answer for A yet when i made x=5 and subtracted new form form the old one I got a difference of ~$\frac{4}{9}$ (should be 0 obviously) I got A=2 B=$\frac{45}{21}$ C=2 How to calculate $\lim_{{x}\to{\infty}}(- e^{-x})$

Homework Statement Show that the sequence of partial sums s_{n} = 1+\sum_{i=1}^{n} \left(\prod_{k=1}^{i}\left( \frac{1}{2} + \frac{1}{k}\right)\right) converges, with n\in \mathbb{N}\cup \{0\} Homework EquationsThe Attempt at a Solution [/B] So we want to find \lim_{n\to\infty} s_{n} =...

It's been a long time since I've attended school, over 33 years ago. So my question may seem basic to many here. I wish to calculate the partial volume of a cylinder for my excel spreadsheet project. The formula I've found is attached. (unable to type it) But I do not fully understand this...

I am looking into Aripiprazole. I am not a medical professional. I am confused by the descriptions of it in Wikipedia: (a) It is a partial dopamine agonist; i.e., it acts like dopamine to stimulate nerve cells, and (b) It is an atypical antipsychotic, i.e., it blocks dopamine (and serotonin)...

Hi. What do I call Instance Classes, Interface, Abstract Classes, Partial Classes, Static Class, Sealed Class collectively? Thanks.

New to set and graph theory and need help on how to approach these exercise questions: For each of the following relations, state whether the relation is: i) reflexive ii) irreflexive iii) symmetric iv) anti-symmetric v) transitive Also state whether the relation is an equivalence or partial...

I have a very basic knowledge of calculus of one variable . In the chapter on heat and thermodynamics , ideal gas law PV =nRT is given . Then the book says, differentiating you get PdV +VdP = nRdT . The book doesn't explain the differentiation step . I think , there are two ways to...

How can I classify a given first order partial differential equations? Are all first order linear PDEs hyperbolic? Quora Link:https://www.quora.com/How-do-I-classify-first-order-PDE-elliptic-hyperbolic-or-parabolic-using-method-of-characteristics

Problem: $${\frac {\partial }{\partial t}}A\left( y,t \right) +6\,\Lambda\,\Omega\, \left( {y}^{2}-y \right) \sin \left( t \right) ={\frac {\partial ^{2}}{\partial {y}^{2}}}A \left( y,t \right)$$ $${\frac{\partial }{\partial y}}A \left( t,0 \right) ={\frac {\partial }{\partial y}}A \left( t,1...

Hi all. Suppose I have the ideal gas law $$P=\frac{RT}{v}$$If I'm asked about the partial derivative of P with respect to molar energy ##u##, I may think "derivative of P keeping other quantities (whatever those are) constant", so from the formula above I get $$\frac{\partial P}{\partial...

Hello . I have problems with two exercises . 1.\lim_{t \to 0 } \frac{2v_1-t^2v_2^2}{|t| \sqrt{v_1^2+v_2^2} } Here, I have to write when this limit will be exist. 2.\lim_{(h,k) \to (0,0) } \frac{2hk}{(|h|^a+|k|^a) \cdot \sqrt{h^2+k^2} } Here, I have to write for which a \in \mathbb{R}_+ this...

Homework Statement Two systems in diffusive equilibrium have equal chemical potentials. We can use this fact to solve the following problem. We begin with a closed system consisting of a liquid such as water in diffusive equilibrium with its vapour. At the start, only the liquid and its vapour...

Homework Statement \int\frac{x^2}{\sqrt{x^2+4}}dx Homework Equations n/a The Attempt at a Solution Letting x=2tan\theta and dx=2sec^2\theta d\theta \int\frac{x^2}{\sqrt{x^2+4}}dx=\int\frac{4tan^2\theta}{\sqrt{4+4tan^2\theta}}2sec^2\theta d\theta=\int\frac{8tan^2\theta...

Homework Statement The entire problem is in the attached picture. I have been checking and double checking for about an hour, found solutions online which agree with my solution, but I cannot find any answer beside -3.697 m/s which is marked wrong by the computer program. Homework Equations Is...

I am reading "Introduction to Set Theory" (Third Edition, Revised and Expanded) by Karel Hrbacek and Thomas Jech (H&J) ... ... I am currently focused on Chapter 2: Relations, Functions and Orderings; and, in particular on Section 5: Orderings I need some help with H&J's depiction of...

I am reading the book: "Discovering Modern Set Theory. I The Basics" (AMS) by Winfried Just and Martin Weese. I am currently focused on Chapter 2 Partial Order Relations ... I need some help with Exercise 1(a) ... indeed, I have been unable to make a meaningful start on the exercise ... :(...

Homework Statement For an analytic function, f(x+iy)=u(x,y)+iv(x,y),u is given by u=(3x^2) -(3y^2). The expression for v, considering K to be a constant is? Homework Equations δu/δx=δv/δy δu/δy=-δv/δx [/B] The Attempt at a Solution My attempt :- u=(3x^2) -(3y^2) δu/δx=6x &...

How does low ambient pressure effect on the thickness of the boundary layer for given flow conditions of gas? In absolute vacuum the thickness of the boundary layer is 0 of course, but it seems that all the boundary layer thickness correlations use the Reynolds number, which doesn’t change much...

Dear Members, I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture. I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have...