Variables Definition and 1000 Threads

Suppose we have a region R in the x-y plane and divide the region into small rectangles of area dxdy. If the integrand or the limits of integration were to be simplified with the introduction of new variables u and v instead of x and y, how can I supply the area element in the u-v system in the...

Hi. Over the years I've read LOT of "popular science" (i.e. non-textbook) books on entanglement, and on the explanations / objections / arguments Einsten, Bohr, Bohm and others had that still remain today. There's one aspect which never seems to get covered in these books and I wondered if...

In a manner analogues to the linearization of functions of a single variable to approximate the value of a function of two variables in the neighbourhood of a given point (x0,y0,z0) where z=f(x,y) using a tangent plane. The tangent plane must pass through the point we wish to approximate z...

I tried saying z = x + iy, then squared both sides so that I would get something that looked like: |z - i|^2 + |z + i|^2 + |z - i||z + i| = 3, where the first two terms are simple but the third term is what I don't know what to do with. I'm wondering if I'm using the wrong approach. For that...

Hi, I understand the underlying concept of changing variables in PDEs (so that we can reduce it to a simpler form), however, I am just not completely clear on the mathematics of it so I have a quick question about it. For example, if we have the transmission line equation \frac{\partial...

For my High School Physics course, I have been tasked to design an experiment investigating the properties of a CD diffraction grating, and we MUST make a graph. Unfortunately, we only have two lasers of different wavelength, so changing the wavelength and measuring ##theta## would be a bad...

Drawing the graph in 3d you see endless "mountains and valleys" which logic tells me there will also be infinite max min points in 2d regardless of where you slice the graph. apparently this is wrong and there is a finite max/min points in R^2/2D. Please note this problem does not have a domain...

Could someone provide me with the intuitive understanding of state of a thermodynamic system? What does state variables/parameters mean?

Hey there! I am current taking an introductory course on PDE's, and our professor hasn't really emphasized last part of solutions from separation of variables. Now its not strictly going to be on the exam, however I remember doing this with ease a few years back, but for some reason now I...

Summary: When ##V (x) = \frac 1 2 mω^2x^2 + mgx## ##H=\frac p 2m +V(x)## Difficulty understanding how these change on variables came about ##y = x+\frac mg mω^2 = x+\frac g ω^2## Apologies if this is not the appropriate thread. I chose this one because even though it's physics, I'm having...

When people graduate and have their degrees in engineering or physics or mathematics or what they may have done, some of these people will use some mathematics, very often which is some-what complicated (or not) arithmetic. Why will some people choose to strictly avoid using variables in the...

As promised, here is the original question, with the integral written in a more legible form.

Given the example g = \frac{GM}{R^{2}}, we may compute the change in field strength if the mass is changed by a small amount dM to be$$dg = \frac{G dM}{R^{2}}$$and also if R is changed by dR,$$dg = \frac{-2 GM dR}{R^{3}}$$If, however, both the mass and radius are changed by a small amount at the...

How do I find the probabilty density function of a variable y being y=ab, knowing the probabilty density functions of both a and b? I know how to use the method to calculate it for a/b - which gives 1/pi*(a²/b²+1) - using variable substitution and the jacobian matrix and determinant, but which...

Summary: Bell's Theorem rules out any hidden variables but does it rule out some finer structure to quantum particles? At larger scales of the universe, we would see entanglement as cloning. For example, two human clones have the same color eyes because their DNA is identical. I've been...

I have taken a look but most books and Online stuff just menctions the First order Taylor for 3 variables or the 2nd order Taylor series for just 2 variables. Could you please tell me which is the general expression for 2nd order Taylor series in 3 or more variables? Because I have not found...

I have a PDE which I have solved numerically using a guass-seidel method, but I want to compare it to the analytical solution. I have used separation of variables to get the general solution, but I need help applying it. The PDE is (1/s)⋅(∂/∂s)[(s/ρ)(∂ψ/∂s)] + (1/s2)⋅(∂/∂Φ)[(1/ρ)(∂ψ/∂Φ)] - 2Ω...

Good morning, I don't understand how the Cepheid variables are used to measure the distance of Stars. Is a member is patient to explain to me thanks

Attempted rewriting acceleration, a, in terms of dv/dt and then separating variables to integrate. This didn’t work... So then I remembered that my gamma factor is also a function of v (!), but then I think I would be required to play around with integration by parts, which seems overly...

this is as far as I get:

Hi, Some of the background related to this question is in this thread, but I've got another question as I'm looking at another problem that has come up with the same application which I'm trying to solve using the equation of meshing for a worm gear and the cutting/grinding tool that creates...

So we know that all the energy originates from the spring: E(spring) = (1/2)kd^2 As the block moves up the ramp, friction does work on the block over a distance of 2d: W = μmgcos(θ)* 2d So subtracting the work done by friction from the spring energy, gives us the energy left, so we'll set it...

1] Let X,Y,Z be independent, identically distributed random variables, each with density $f(x)=6x^5$ for $0\leq x\leq 1,$ and 0 elsewhere. How to find the distributon and density functions of the maximum of X,Y,Z.2]Let X and Y be independent random variables, each with density $e^{-x},x\geq...

Smolin latest book about the quantum is quite interesting. Its called "Einstein Unfinished Revolution: Search for What Lies Beyond the Quantum" and he has a new theory or interpretation. Id like to know what you make of it. The theory is very simple. Similar views produce QM. May i know how this...

I am given the following: $$u = (x,t)$$ $$\frac{\partial^2 u}{\partial t^2} - c^2\frac{\partial^2 u}{\partial x^2} = 0$$ and $$E = x + ct$$ $$n = x - ct$$ I need to solve for $$\frac{\partial^2 u}{\partial x^2}$$ and $$\frac{\partial^2 u}{\partial t^2}$$ using the chain rule.How would I even...

Quadratic equation Ax^2+Bxy+Cy^2+Dx+Ey+F=0 is (a) elipse when ##B^2-4AC<0## (b) parabola when ##B^2-4AC=0## (c) hyperbola when ##B^2-4AC>0## I found this in Thomas Calculus. However for some values of parameters ##A=17##, ##C=8##, ##B=\sqrt{4 \cdot 17 \cdot 8}##, ##D=E=0##, ##F=20## I got just...

Hey Guys, exercise: "It is desired to study the first excited state of 16O which is at energy of 6.049 MeV. Using the (alpha, n) reaction on target of 13C, what is the minimum energy of incident alphas which will populate the excited state? So, i suggest to define first the reaction equation...

If we would learn (somehow) that the pilot wave theory is false, that there are not even "non local" hidden variables, would this lead to a paradigm shift in physics? I ask because it would mean that a Laplace demon wouldn't even in theory able to predict the exact future motions of particles...

Can all the multiplexers work for any number of variables given? For example can I make a 16:1 multiplexer for 2 variables inputs, A and B?

I was told to generate these variables (m, C, alpha, wind velocity) normally distributed and compare the random data with the result and then tell, which of the variables has the most impact. Here I am stuck, tried to compare variances, kurtosis and skewness of the data (the original variables...

Quotient rule: z= f/g ------ z'= (f'g - g'f)/g^2 starting with finding the derivative in respect to x, i treated y^2 as constant 'a': z'= [(a*2x*cos a*x^2)(sin a*x^2) - (- a*2x*sin ax^2)]/cos(a*x^2)^2= [(a*2x*cos a*x^2)(sin a*x^2)+(a*2x*sin ax^2)]/cos(a*x^2)^2 For the derivative in respect to y...

When using the separation of variable for partial differential equations, we assume the solution takes the form u(x,t) = v(x)*g(t). What is the justification for this?

Form solid state physics, we know that the volume of k-space per allowed k-value is ##\triangle{\mathbf{k}}=\dfrac{8\pi^3}{V}## ##\sum_{\mathbf{k}}F(\mathbf{k})=\dfrac{V}{(2\pi)^3}\sum_{\mathbf{k}}F(\mathbf{k})\triangle{\mathbf{k}}##...

So i first need to come up with the sample space, X, and Y. Well I would guess that the random variables here are N1 and N2 and thus X = N1 and Y = N2. Now i need to make these random variables a function of L. I don't know what L should be but I would guess it is the outcome of a 1ms interval...

How to answer this question $\rightarrow$https://stats.stackexchange.com/q/398321/72126

Hi everyone. I'm currently trying to create a function/expression based on several variables. I've so far figured out the rules that the variables should follow but I'm struggling to put them together into a formula. I'm hoping that someone here might tell me if this is even possible, and give...

Homework Statement Given that ##x=\phi (t)##, ##y=\psi(t)## is a solution to the autonomous system ##\frac{dx}{dt}=F(x,y)##, ##\frac{dy}{dt}=G(x,y)## for ##\alpha < t < \beta##, show that ##x=\Phi(t)=\phi(t-s)##, ##y=\Psi(t)=\psi(t-s)## is a solution for ##\alpha+s<t<\beta+s## for any real...

Homework Statement The assignment is to transform the following differential equation: ##x^2\frac {\partial^2 z} {\partial x^2}-2xy\frac {\partial^2 z} {\partial x\partial y}+y^2\frac {\partial^2 z} {\partial y^2}=0## by changing the variables: ##u=xy~~~~~~y=\frac 1 v##Homework Equations...

Hi all, I have learned the very basics of entanglement (discrete, 2 particle systems) and was hoping that someone can recommend introductory (undergrad-level) material for continuous-variable, 2 particle entanglement. Stuff I have found online so far (like this...

If X and Y are independent gamma random variables with parameters $(\alpha,\lambda)$ and $(\beta,\lambda)$, respectively, compute the joint density of U=X+Y and $V=\frac{X}{X+Y}$ without using Jacobian transformation. Hint:The joint density function can be obtained by differentiating the...

Hey, I'm tutor for theoretical physics for first year students and I found a question that I couldn't answer so far. It's about the rocket equation. I tried to derive the acceleration without using infinite small variables, but somehow there is one term left that shouldn't be there. In the...

Let X and Y be independent normal random variables each having parameters $\mu$ and $\sigma^2$. I want to show that X+Y is independet of X-Y without using Jacobian transformation. Hint given by author:- Find their joint moment generating functions. Answer: Now Joint MGf of...

Homework Statement I am always confused about how to correctly write the functions U, H, F, G when they're not depending on the usual variables p, V, T, S - same question for Q and W. For example, we have to calculate the temperature variation of a small surface of water when we isentropically...

Hey there, trying to figure out how to solve this integral (see picture). I've never seen an integral written in this way before. I've tried to integrate the x-part first and then the y-part and vice versa but they both gave the wrong results.

I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 1.7: Derivatives in Several Variables as Linear Transformations ... I need some help in order to understand some...

Homework Statement A plane travels 3000 mi in 4 hours, when the wind is favorable the plane averages 900 mph. When the wind is unfavorable the wind averages 500 mph. During how many hours was the wind favorable.Homework EquationsThe Attempt at a Solution To me this looks like a simple equation...

Homework Statement lim (x,y)->(0,0) (ln(1+2x^2+y^2))/(x^2+3y^2)^2 Homework Equations The Attempt at a Solution i've been tought that i have to find another equation always bigger than this one that goes to 0 at (0,0) to find a solution. or if the solution doesn't exist, try to find two paths...

Hello,I have been going through Griffiths’ Intro To Quantum Mechanics in an attempt to self-teach myself some quantum mechanics. I am currently in section 3.4 (Generalized Statistical Interpretation) I am seeing a “step” occur more than once. When I first came across it, while I didn’t...

In transforming an integral to new coordinates, we multiply the “volume” element by the absolute value of the Jacobian determinant. But in the one dimensional case (where “change of variables” is just “substitution”) we do not take the absolute value of the derivative, we just take the...