Gradient Definition and 723 Threads

hi all, do you know what is the gradient of a tensor looks like? I mean the del operator on a second order tensor, not the divergence of the tensor. And actually I need them in polar coordinates.. I have been searching so hard in web, but I can't find anything useful. Please help.

Homework Statement Calculate the gradient vector at the point S for the function, f(x,y,z)=x-\sqrt{z^2 - y^2}; S(x,y,z)=(4, 8, -6). 2. The attempt at a solution \frac{\partial f}{\partial x} = 1 \frac{\partial f}{\partial y} = \frac{y}{\sqrt{z^2-y^2}} \frac{\partial f}{\partial z} =...

hi. the is it true that if \vec{m} is a constant vector, then \nabla \cdot \vec{m}=0?

Wave speed changes only when medium changes. But so far, all I've seen is a definite boundary behavior where one medium abruptly ends and another one begins. What happens if there is a gradient. For example, what happens when a wave is passed through a rope with a density gradient. It is very...

Does anybody know, or know where to find, the expressions for the gradient and/or divergence in hyperspherical coordinates. Specifically, I'd like to know \nabla \cdot \hat{r} in dimensions higher than 3.

Homework Statement Let f(x,y,z)= |r|-n where r = x\hat{i} + y\hat{j} + z\hat{k} Show that \nabla f = -nr / |r|n+2 2. The attempt at a solution Ok, I don't care about the absolute value (yet at least). I take partial derivatives of (xi + yj + zk)^-n and get \nabla f =...

1. A rod carrying a uniform charge distribution is bent into a semi circle with the center on the orgin and a radius R. Calcualte the Electric field at the center of the semi circle using the electric potential expression found in part a 2. E = -(gradient)V 3. The electric...

Homework Statement The elevation of a mountain above sea level at (x,y) is 3000e^\frac{-x^2-2y^2}{100} meters. The positive x-axis points east and the positive y-axis points north. A climber is directly above (10,10). If the climber moves northwest, will she ascend or descend and at what...

Homework Statement Consider the function f (x,y). if you start at the point (4,5) and move to the point (5,6) . the directional derivative is 2. Starting at the point (4,5) and moving toward the point (6,6)gives a directional derivative of 3.Find grad f at the point (4,5) . Homework...

Homework Statement View the curve below as a contour of f(x,y). (y-x)^2 + 2 = xy - 3 Use gradf (2,3) to find a vector normal to the curve at (2,3). Homework Equations The Attempt at a Solution I am not sure how do I get the vector normal to the curve, is it using a cross...

Homework Statement First problem: Let f(x,y) = x-y and u = vi+wj. In which direction does the function decrease and increase the most? And what u (all of them) satisfies Duf = 0 Second problem: Let z = f(x,y), where x = 2s+3t and y = 3s-2t. Determine \partial{z^2}/\partial{s^2}...

Homework Statement Suppose, in the previous exercise, that a particle located at the point P = (2, 2, 8) travels towards the xy-plane in the direction normal to the surface. a) Through which point Q on the xy-plane will the particle pass? b) Suppose the axes are calibrated in...

The temperature in an auditorium is given by T = x2 + y2 - z. A mosquito located at (1,1,2) in the auditorium desires to fly in such a direction that it will get warm as soon as possible. In what direction must it fly? I know that the gradient of T will point to the direction where the...

Homework Statement 1. Calculate the gradient of the curve y = 2x3 - 5x2 + 46x + 87 at the point where it crosses the x-axix. 2. Show by differentiation and solving a quadratic equation, that there are no points on the above curve where the gradient is zero.Homework Equations y = 2x3 - 5x2 +...

Define f: R^{2} \rightarrow R , by f(x,y) = \int^{sin(x sin(y sin z))}_{a} g(s) ds where g:R -> R is continuous. Find the gradient of f. I tried using the FTC, and differentiating under the integral, but did not get anywhere, thanks for any suggestions.

I am given some function f(x,y) and I am asked to find what the maximal rate of change is at some point (x0y0) and the direction in which it occurs. Is this correct: Maximal rate of change=|\nabla{f}(x_0,y_0)| And for the direction, if \nabla{f}(x_0,y_0)=<a\, ,b\,> then the direction is...

Earlier today, I came up with an explanation of why 0^0 is undefined in terms of properties of exponentiation. In it, I was treating exponentiation as a function from R^2 to R. Then, it occurred to me that the gradient of a function f(x,y) = x^y would be a horrible nightmare. Perhaps something...

I'm doing a selfstudy on relativistic electrodynamics and stumbled over a problem (which i find rather important) i can't solve. It's concerning problem 12.55 in Griffiths introduction to electrodynamics. One needs show that the four gradient: \frac{\partial}{\partial x ^\mu} functions as a...

Greetings, I'm having trouble deciding what to do, and in what order for this question: Suppose F = F( x, y, z ) is a gradient field with F = \nablaf, S is a level surface of f, and C is a curve on S. What is the value of the line integral (over C) of F.dr ? I think I'm a little confused...

Hello, I was messing around with subscript summation notation problems, and I ended up trying to determine a vector identity for the following expresion: \overline{\nabla}(\overline{A}\cdot\overline{B}) Here are my steps for as far as I got: \hat{e}_{i}\frac{\partial}{\partial...

Hi, May i know the physical meaning of the following: (1) Curl of a vector field A(x,y,z) (2) divergence of a vector field A(x,y,z) (3) directional deriative of G(x,y,z) (4) gradient of a scalar field G(x,y,z)

The length contraction in special relativity says that a rod moving along its axis will appear shorter by γ to a stationary observer. I think, however, not only the rod will appear shorter, but also each small segment of the rod will show its snapshot of different time as in the moving frame, in...

What is the difference between strain rate and velocity gradient of a Newtonian fluid?

Hi. Is it possible for two separate points on an equipotential surface to have two different values for the force field? eg, point A and point B lie on an equipotential surface, but the equipotential surface spacing is much denser at A than at B - so the force field at A as the gradient...

Does anyone know how to draw a gradient field? For example, how do you draw one of f(x,y)=xy^2

Find the gradient of F(s,t) = f(x(s,t), y(s,t)) where f(x,y) = y/x x = s^2 + t^2 y = s^2 - t^2. I'm not sure how to even start the problem. Could someone point me in the right direction?

Homework Statement f(x)=(1/2)*(x^T)*(A)*(x)-(x^T)*(b) Show that the gradient of f(x) is (1/2)*[((A^T)+A)*x]-(b) where x^transpose is transpose of x and A^transpose is transpose of A. Note: A is real matrix n*n and b is a column matrix n Homework Equations The Attempt at a...

ok, quick and dirty and stupid question about calculation rules with 4 gradients: consider the Klein Gordon Lagrangian L_{KG} = \frac{1}{2} \partial_{\mu}\Phi\partial^{\mu} \Phi - \frac{1}{2} m^2 \Phi^2 . Why is \partial_{\mu} \left( \frac{\partial L_{KG}...

(Sorry, the title should read "...why curl of gradient of a scalar "function" is zero) Of course I know how to compute curl, graident, divergence. Algebrically I know curl of gradient of a scalar function is zero. But I want to know the reason behind this...and also the reason why gradient of...

First off, this is not a homework problem, but rather is an issue that I've had for a while not and haven't quite been able to reason out to my satisfaction on my own. u-vector = ui + vj + wk What is grad(u-vector)? I know what the gradient of a function is, but this is the gradient of a...

Hi, There is some issue about gradients that disturbs me, so I'd be glad if you could help me figure it out. Say I have a scalar field \phi(\mathbf{r}), that is not yet known. What I know is a function that is the gradient of \phi, so that \mathbf{F}(\mathbf{r}) = \nabla\phi(\mathbf{r}). I...

Can anyone tell me what a linear salt gradient is?

Just a really quick sanity check. This equation... \nablasU = \nablaU - n*(n \bullet \nablaU) ...the correct equation for the surface gradient given \nablaU is the gradient of the surface and n is the normal unit vector?

This is a general question. If we have a parametric equation r(u,v) and we take r_u and r_v, then take their cross product, does it give us the gradient vector? Or just a vector parallel to the gradient vector?

Hello, I need help. The topic is a gradient in spherical coordinates. In cartesian it is clear but in spherical coordinates I have two terms which I don't understand from where they come. Okay, I have a scalar field in spherical coordinates: \Phi = \Phi(r, \theta, \phi) I thought...

Hi everyone, This might belong in the quantum mechanics section, so I apologize if I placed this thread in the wrong place. My question is: how do I calculate the gradient of a multiparticle wavefunction? For example, suppose that a wavefunction \psi describing the probability...

A bit of a problem. My book teaches me that E = -(dV/dx), where E is the electric field strength, V is the electric potential, and x represents displacement. But, it also suggests along with the above formula that E = -(V/d) and displays a circuit with a battery of p.d. V and two parallel...

I am given z = 32 - x^{2} - 4y^{2} Starting at the point (3,2) in i + j direction, find if you are going up or down the hill and how fast. The way I thought to proceed was that the gradient would tell me if I was going down or up hill and that \left|\nabla z \right| would give me...

I am trying to recreate the Stern-Gerlach experiment and am having trouble trying to calculate the gradient magnetic field. I am using two magnets with one having a sharp edge and the other flat. I have calculated what the deflection will be of the electron will be in terms of the gradient...

In the context of height fields, the geometric meaning of partial derivatives and gradients is more visible than usual. Suppose that near the point (a, b), f(x, y) is a plane (the above figure). There is a specific uphill and downhill direction. At right angles to this direction is a direction...

Homework Statement The gradient of the curve is: \frac{9-x^{2}}{(9+x^{2})^{2}} Find the turning points on the curve Homework Equations The Attempt at a Solution Well for a turning point the gradient of the curve = 0 \frac{9-x^{2}}{(9+x^{2})^{2}} = 0 but now what to do. in...

\nabla\stackrel{\rightarrow}{A} when a gradient operater act on a vector,what is it stand for ?

[SOLVED] Surprising Gradient not 'Surprising Enough' Homework Statement Q] Sketch the vector function and v = \frac{\hat{r}}{r^2} and compute it's divergence. The answer may surprise you... can you explain it? ['r' is the position vector in the Euclidean space] Homework Equations...

I'm trying to understand why the gradient vector is always normal to a surface in space. My textbook describes r(t) as a curve along the surface in space. Subsequently, r'(t) is tanget to this curve and perpendicular to the gradient vector at some point P, which implies the gradient vector to be...

" find, in terms of a and k, the gradient of the graph y = a - k/x at the point where it crosses x axis." ok i worked out dy/dx = k/x^2 and x = k/a when y = o. now what do i do. =( thx for help in advance

Homework Statement if \phi = rk/r^{3} where r=xi + yJ + zk and r is the magnitude of r, prove that \nabla\phi = (1/r^{}5)(r^{}2k-3(r.k)r so i differenciated wrt x then y then z and tried to tidy it all up but i got1/rClick to see the LaTeX code for this image(-3(r.k)r) When i...

i need to know the formula for calculating the uncertainty of a gradient from a graph. the gradient is being used to calculate the moment of inertia but i can't calculate the error in my I cause i don't know how to calculate the error in my M! when i did the experiment, i assumed the error to...

I'm looking for the most efficient (practical, not theoretical) way to turn a heat gradient of unknown measure (at least roughly from -10°F through 100°F) into energy. Probably some expert arround? Any engineers here working on something similar?

a very dilute orange juice flows along a smooth tube (0.010m in diameter) with a maximum flow rate of 0.1m/s. a) State the assumptions needed to solve the problem b) Calculate the pressure gradient Equations: Vmax = (Change in P * R^2)/(4*viscosity*L) Reynolds number = (density*D*v)/viscosity...

Homework Statement I have 25 pairs of values. I have a gradient and want to test if this gradient is significantly different from 1. Which stats test do I use? I thought of using a one-sample t-test, but how are you meant to put 25 gradients in the test!? thanks...