Variables Definition and 1000 Threads

I'm looking back at a previous thread here, in hopes of an answer regarding acceleration of engine RPM, and I have found something that might have answered it, the first post on this page: https://www.physicsforums.com/threads/accelerator-pedal-and-rpm.760572/page-4 (I suggest you don't go...

Homework Statement Suppose I have the following expression: (v \frac {\partial}{\partial r} ) f(r,v) I want to obtain: \frac {\partial \hat{f}(z,x)}{\partial z} Homework Equations x \rightarrow v/v0 z \rightarrow (r-r0)/H H \rightarrow \frac{k_{b} T} {m g } \hat{f}(z,x) = x^2...

haruspex submitted a new PF Insights post Conceptual Difficulties in the Roles of Variables Continue reading the Original PF Insights Post.

Today, I had a class on Complex analysis and my professor wrote this on the board : The Laplacian satisfies this equation : where, So, how did he arrive at that equation?

I am trying to solve a Duffing's equation ##\ddot{x}(t)+\alpha x(t)+\beta x^3(t)=0## where ##\alpha## is a complex number with ##Re \alpha<0## and ##\beta>0##. The solution can be written as Jacobi elliptic function ##cn(\omega t,k)##. Then both ##\omega## and ##k## are complex. The solution to...

The overall question is on non steady fluid mechanics however the part on stuck on boils down to the two equations below, which I am unable to solve. X = 122.3 (2 - Y) Y= 0.18 * SQRT( 100 + X ) the text states the equations are satisfied by Y = 1.903 and X = 11.82. To prove this isn't a...

Below is an example problem from my textbook. I don't fathom the highlighted portion where they replace the y variable with x in accordance with fig. 3.6.3? Please help Thanks

Liquid is flowing into a small tank which has a leak. Initially the tank is empty and, t minutes later, the volume of liquid in the tank is V cm3 . The liquid is flowing into the tank at a constant rate of 80 cm3 per minute. Because of the leak, liquid is being lost from the tank at a rate...

Homework Statement Homework EquationsThe Attempt at a Solution I managed to do the first part of the question. But I'm not sure how to find u(x,t) with that initial condition. The solution says; "since ##u(x,0) = \sum_{n=1}^\infty a_{n}\sin{(n\lambda x)}## Then it follows by linearity that...

Homework Statement Solve in ##\mathbb{Z}^2## the equation ## x^2 -y^2-x+3y = 30 ## Homework EquationsThe Attempt at a Solution Hello, can you tell me if this is correct please ? The equation is equivalent to ## (x-y+1) (x+y-2) = 28 ##. I call ## u = x-y+1 ## and ## v = x+y-2 ## We have that...

(n-1)! = (x2 + x)( (n/2)! (n-2/2)! Any idea how to solve this? I tried to solve for x but got stuck. Could you multiply out the factorials?

Hi, I'm trying to identify the free variable and binding occurrence but I'm not sure if they're right in lambda calculus. $x$ $\lambda x.x$ $(\lambda a.z)a$ $\lambda a.za$ $(\lambda n.n)z$ $\lambda z.(\lambda y.(\lambda x.x)y)z$ $(\lambda t.((\lambda t.(\lambda t.t)t)t))t$ Then for free...

Homework Statement Consider the function of two variables: u(x,y) = f(x-y) + g(x+(1/3)y) where f(s) and g(t) are each arbitrary functions of a single variable. Using the change of variables: s = x-y t = x-(1/3)y use the chain rule to determine the first and second derivatives of u with...

Homework Statement Hi I am given the functional I am asked to show that if and with an appropriate value for that Homework Equations [/B]The Attempt at a Solution So I get If I set then I get I think that it is correct but what about the factor of 2?

Hey! :o How can we prove by induction the relation $A(x,y)>y, \forall x,y$ ?? (Wondering) When we have to prove a relation $P(n), n\geq 0$, we do the following steps: we show that it stands for $n=0$ we assume that it stands for n=k (Induction hypothesis) we want to shw that it...

Homework Statement In the book it gave the example for standard change of variables as, z = x / 1 + x or equivalently x = z / 1 - z , then dx = dz / (1 - z)^2 , thus (2) 1 / (1 - z)^2 f (z / 1 - z) dz (3) This is what I am trying to accomplish but with the...

Hi, I'm trying to solve this exercise but I really don't know how 1. Homework Statement Let X1, X2,.. be a sequence of iid random variables following a uniform distribution on (0,1). Define the random variable N≥2 as the first point in which the sequence (X1,X2,...) stops decreasing. i.e If...

I am using the text by Farlow to study elementary methods of solving PDEs, and there is a point in his illustration of separation of variables where I am not seeing something. I am clear on everything that comes after and before this point, but after having returned to a certain step a few times...

Hey I am trying to evaluate d/dx, d/dy and d/dz of a wavefunction defined on a grid. I have the wavefunction defined on equally spaced points along three axes a=x+y-z, b=x-y+z and c=-x+y+z. I can therefore construct the derivative matrices d/da, d/db and d/dc using finite differences but I...

I'm talking about this: http://www.cs.cornell.edu/courses/cs6650/2008fa/images/thumb_EL.jpg In the derivation when you minimize action you assume that all the variations in coordinates are independent and thus conclude that each term has to be zero. When this isn't the case anymore one doesn't...

Hi. I would like to know which variables in the wave function are constant (in this local context) and which are not. The wave number for instance varies in the article I was reading (WKB approximation). Why is this so? What other variable in the wavefunction can vary? Please help me as I am...

Hi There, I'm a new member, so apologies if I've posted this in the wrong area. I've been working through the ASME STS-1-2006 Steel Stack Standard, particularly the Vortex Shedding section. I've come across this nasty integral which is doing my head in, and we wondering if anyone would mind...

Hello! (Smile) We have the differential equation $y''+ \frac{p}{x} y'+ \frac{q}{x^2}y=0, x>0$ and we set $z=\log x$. Then $y'=\frac{dy}{dx}=\frac{dy}{dz} \frac{dz}{dx}=\frac{1}{x} \frac{dy}{dz}$ $y''=\frac{d^2y}{dx^2}=\frac{d}{dx}\left( \frac{dy}{dx} \right)=\frac{d}{dx}\left( \frac{1}{x}...

Hello! I've to solve y(y')^2+2xy' -y=0 by letting y^2= r^2-x^2 but this change of variable has thrown me. Could someone please help?

Homework Statement A weather balloon is filled with Helium gas and released from the ground. It goes up 18km and achieves a diameter of 15m. Determine if the following values are greater than zero, less than zero, or equal to zero: ΔV, ΔP, ΔT, ΔU, ΔH, Ssys, surr, Stot Homework Equations ΔU =...

Homework Statement Show that the equations xy^2+zu+v^2=3 x^3z+2y-uv=2 xu+yu-xyz=1 can be solved for (x,y,z) as functions of (u,v) near the point (x,y,z,u,v)=(1,1,1,1,1) and find dy/du at (u,v)=(1,1) Homework Equations Multivariable calculus differentiation 3. The Attempt at a Solution I...

Homework Statement Suppose that A, B, C are independent random variables, each being uniformly distributed over (0, 1). ) What is the probability that all the roots of the equation Ax2 + Bx + C = 0 are real? Homework Equations (b) What is the probability that all the roots of the equation...

Homework Statement Use a change of variable to show that \int_0^{\infty} \frac{dx}{1+x^2} = 2\int_0^1\frac{dx}{1+x^2} Please note: the point of this exercise is to change the bounds of the integral to be finite to allow numerical estimation, as opposed to directly solving the integral...

Hey MHB ! I've got a question that I am clueless how to proceed Prove that $$\Large \lim_{(x,y)\to (0,0)}(1+x^2y^2) ^{\frac{-1}{x^2+y^2}} = 1$$ Any hint would be appreciated.

How do we know that separable solutions of Schrodinger equation (in 3d) form a complete basis? I understand that the SE is a linear PDE and therefore every linear combination of the separable solutions will also be a solution , but how do we know that the converse, i.e 'every solution can be...

\chi_m = - \frac{Z e^2 n \mu_0}{4 m} <p^2> My understanding is that n = N/V, where the volume is the volume of a unit cell containing Z electrons (in this case n = \frac{1}{a^3}). The m in the denominator is related to the larmor frequency and, for a hydrogen atom, should be the mass of a...

Bohm writes in his 1951 book "Quantum Theory" (p623): "We conclude then that no theory of mechanically determined hidden variables can lead to all the results of quantum theory". He bases his argument on the uncertainty principle. Presumably the argument is not correct, since Bohm himself...

Homework Statement Find the principle argument Arg z when z = (sqrt(3) - i)^6 Homework EquationsThe Attempt at a Solution I'm sorry to say that I'm not sure how to solve this problem. It's my understanding that what this question is basically asking me to do is find theta such that...

Hi all, I'm trying to show that a particular function of two variables is concave for all positive values of x and y. I'm pretty sure it is, but I haven't been able to prove it. The function is (1-et(y-x))xy)/(x+et(y-x)y) t is a positive parameter, and as mentioned, x and y are always...

Homework Statement Say I calculated a probability density of a system containing m spins up (N is the total number of particles). The probabilities of being up and down are equal so this is easy to calculate. Let's call it ##\omega_m##. Then we define magnetization as ##M=2m-N## and it asks me...

I am a little confused about how variables are related to distributions as one moves from descriptive statistics to inferential statistics. I know that a variable in descriptive statistics is some measurable characteristic of some phenomenon, and its distribution is some description (table or...

So, I have some questions regarding 'dimensions' and 'parameters' in physics. (there are differences in the meaning between physics and mathematics, as far as I understand it) ---- As far as I understand it, we live in a 4-dimensional world, consisting of 3 space and 1 time dimensions. Yet we...

I'm just doing some geometry and I can't remember how to find the maximum values of two variables in the same equation. Like, if you differentiate the equation partially for one, then again from the beginning partially for the other and add them together or something. The equation is something...

Homework Statement Here is a small part of an EESEE data set, "Nutrition and Breakfast Cereals," that describes the nutritional content per serving of 77 brands of breakfast cereals: What are the individuals in this data set? For each individual, what variables are given? Which of these...

Variable Units x Meters (m) v Meters per second (m/s) t seconds (s) a Meters per second squared (m/s^2) These variables appear in the following equations, along with a few numbers that have no units. In which of the equations are the units on the left side of the equals sign consistent with...

Statistical probabilities of a objects qualities as is emerging out of infinite variable states. Can an equal emergence occur again, and as a unavoidable fact of infinites result in endless occurrences, given infinite chance in an eternal cosmos? I say no. If the (falsely inferred as)...

I have asked the same question on math stackexchange under the moniker "anonymous," since I do not wish to be known there. I will try my luck here.$$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ I don't understand, we say: $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ Then we say: $$I =...

Homework Statement $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ Homework Equations Below The Attempt at a Solution $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ I don't understand, we say: $$I = \int_{-\infty}^{\infty} e^{-x^2} dx$$ Then we say: $$I = \int_{-\infty}^{\infty} e^{-t^2} dt$$...

I was arguing with a friend over the whole 'big data' trend and how people are looking to get answers to questions by amassing many samples over many variables and hoping to mash it together somehow. (Under the assumption not only of lots of correlations to search over but also that...

Homework Statement So I'm doing a question from one of my past exams as attached, there are no copy right issues with this document that I know of and have asked my lecturer who wrote the exam and he said I am welcome to upload it. The question is 1)b)iv), my attempt is attached. I end up with...

Homework Statement If Y=X1+X2+...+XN prove that <Y>=<X1>+<X2>+...+<XN> Homework Equations <Y>=∫YP(Y)dY over all Y. The Attempt at a Solution I only seem to be able to show this if the Xi are independent, and I also think my proof may be very wrong. I basically have said that we can write the...

I've attached the question along with its solution. It seems fairly simple yet the answer doesn't seem quite right to me. It appears as though they let downwards be + and that ## m\frac{dv}{dt} = mg + 0.4v## where v is negative since the ball is on its way up and there is a + instead of a - on...

I am new to the world of Science & Mathematics but am eager to learn all I can. I go to my local library and open up books on the topic such as Physics, Engineering and Electronics and there are swathes of formulas all of which I don't understand. I stare at them wondering what keys they must...

Homework Statement Z = X - Y and I'm trying to find the PDF of Z. Homework Equations Convolution The Attempt at a Solution Started by finding the CDF: Fz(z) = P(Z ≤ z) P(X - Y ≤ z) So I drew a picture So then should Fz(z) be: since, from my graph, it looks as though Y can go from...

If $$u=\frac{1}{2} E^2$$ and $$v=\frac{1}{2}B^2$$ and we have that $$\frac{\partial L}{\partial u} \frac{\partial L}{\partial v} = -1$$ The author says: to obtain explicit solution of the above, one must resort to techniques such as separation of variables in particular coordinate systems. For...