Gradient Definition and 723 Threads

Hi all. I have a question that I am thinking about for a couple of days. Let's consider the time-independent Schroedinger equation for a molecule: H0 [psi> = E0 [psi> Now, we know that the unperturbed Hamiltonian consist of electronic kinetic energy operator, electron-electron repulsion...

Homework Statement [PLAIN]http://img576.imageshack.us/img576/4968/vec0.jpg The Attempt at a Solution (i) is not irrotational and (ii) is - I wish it was the other way round! Can anyone help my construct a potential function \phi (x,y,z) for (ii)?

greetings in a scalar gradient why does the unit vector has appeared?scalar gradient only represent the change in that scalar quantity along x,y and z axis.then why unit vector along x, y and z comes in picture? advanced thanks.

The question is as follows: A circular tube of radius 'a' bifurcates into two tubes with equal radii 'ka', where k is a dimensionless coefficient. Derive an expression for the ratio of the pressure gradient in each bifurcated tube to that in the initial tube in terms of 'k'. I'm not sure...

So I am working in spherical coordinates and to find the gradient I have the eqn G-1d\phi where \phi is a scalar function Then I am supposed to compute in terms of {em} and {wm}. I am just confused what it means to compute in terms of? Do i have to convert the co and contra vectors...

Homework Statement Hi Can anyone explain the following statement: When the tangent is parallel to the y-axis it has infinite gradient Would this be the same condition for a tangent parallel to the x axis? I came across it in the Edexcel C4 textbook. Cheers Homework Equations...

Homework Statement A table of values of a function f with continuous gradient is given. Find the line integral over C of "gradient F dr" where C has parametric equations x = t2 + 1, y = t3 + t, 0<=t<= 1. Sorry, don't know latex. But here's a picture of the table and values...

is the normal just grad(f(x0,y0,z0))? If so, how exactly does this work out to be so? Explain? Thanks... :D & is the calculus section the most appropriate place to put this question? thanks again. :)

"Gradient Expansion" Hi, I'm having trouble finding the origin of a series expansion of the form: f(x)= A_i \partial_i f(x) + B_{ij} \partial_{i} \partial_j f(x) + C_i [\partial_i f(x)]^2 + \ldots or the similar expansion f(x)= A \nabla f(x) + B \nabla^2 f(x) + C \vert \nabla...

Hello I was wondering if centrifugal force had a gradient, what i mean by this is this:- A train is traveling on a straight section of track with no centrifugal force. The train then travels along a transition, as the train travels along the transition, the centrifugal force builds up...

There is a temperature difference and we know the transition of the working fluid (from the hot chamber to the cold one) is isometric. So either there must be a pressure difference, or the number of molecules must be smaller; however, this can't be the case since eventually all the gas must move...

1. While descending Mt. Everest you are caught in a sudden snowstorm. Unable to see more than a few feet in front of you, you determine through careful observation that if you travel three meters northwest you climb 1/2 meter, and if for every two meters you travel northeast you descend 1/4...

Dear All I am having trouble understanding the gradient vector of a scalar field (grad). I understand that you can have a 2D/3D space with each point within that space having a scalar value, determined by a scalar function, creating a scalar field. The grad vector is supposed to point in...

Homework Statement The shape of a hill is described by the height function: h(x,y) = \frac{1}{\sqrt{2+x^2+y^4}} a) find the gradient \nabla h(x,y) b) find the maximum slope of the hill at the point \bf{r_0 = i+j} [or (x,y) = (1,1)] c) If you walk NorthEast (in the direction of the...

Homework Statement Well the problem is a electromagnetism problem: I need to find the charge density. Given E= kr^3 r^ Homework Equations formula is gradient E=p/e0 The Attempt at a Solution They got the gradient of E to be 1/r^2 (d/dr) (r^2 Er) i have no idea how they did...

Hi, I've gotten the conjugate gradient method to work for solving my matrix equation: http://en.wikipedia.org/wiki/Conjugate_gradient_method Right now I'm experimenting with the preconditioned version of it. For a certain preconditioner however I'm finding that is zero, so no proper update...

gradient vectors and tangent lines! If f(x, y) = xy, find the gradient vector f(3, 7) and use it to find the tangent line to the level curve f(x, y) = 21 at the point (3, 7). I already found the gradient vector to be <7, 3>, Maybe I am missing something obvious, but I have no clue how to...

I just started learning about cellular respiration and I'm not clear as to what the word "gradient" means. I see it tied to many terms such as electrochemical gradient, proton gradient and ion gradient. Is a gradient just a space or "field" with varying concentrations of something (protons...

In Marion & Thorton problem 1.29 asks to find the angle between two surfaces (x^2 +y^2 + z^2)^2 = 9 and x + y + z^2 = 1 at a point. The solution takes the gradient of (x^2 +y^2 + z^2)^2 - 9 and x + y + z^2 - 1, and using the dot product between the two vectors at that point gets the angle...

How will i find the gradient of a vector? i know that gradient is only for scalar to produce a vector? i am confuse since del operator is a vector how will i find the gradient of a vector. How can i multiply a del operator and vector

We've got a table of periods (in seconds) and their corresponding wavelengths for creating resonance in a closed pipe. I've been told that plotting a graph of period (on x axis) vs wavelength, and finding the gradient of that linear line will tell me the speed of sound in air. I can do that...

Hi All, I have been trying to understand some fluid mechanics in a research paper and have been wrestling with the mathematics for quite some time now without success. I want to derive gradient operator with following coordinate system in R^3 space Let and arbitrary curve C be locus of...

If the first derivative of a function represents the gradient of the tangent line... What does the second derivative represent? Thanks in advance James

For a tangent plane to a surface, why is the normal vector for this plane equal to the gradient vector? Or is it not?

IMPORTANT! ---- what is the geometric intepretation of the gradient vector? Assume the situation in which I have a slope, a component of a function dependent on x and y, which is at an angle to the xy plane. The gradient vector would be perpendicular to the tangent plane at the point in which i...

Homework Statement When i see the upside down triangle squared . Is this the Gradient squared, or the second derivative of the x , y and z components And this is the Laplace operator

I have derived that, when there is a temperature difference (gradient) in a gas (consider a long tube with one end maintained at 100oC and other end maintained at 0oC), there will be a pressure gradient (something similar to Bernoulli's law). Please see the attached document or this link for...

For a function ƒ defined on an open set U having the point X:(x1,x2,...,xn) and the point ||H|| such that the point X + H lies in the set we try to define the meaning of the derivative. \frac{f(X \ + \ H) \ - \ f(X)}{H} is an undefined quantity, what does it mean to divide by a vector...

"Definition" of Curl. Can anyone derive the gradient operator? Can anyone prove why this equality is true? http://en.wikipedia.org/wiki/Curl_%28mathematics%29#Definition Wikipedia says it is defined, however that's BS since the gradient operator was already defined so this needs to be proven...

Homework Statement Find the gradients of the following functions: When I say gradient, I'm not just differentiating the functions, apparently I have to do it this way (because it's in my physics book) f(x,y,z) = x^2 + y^3 + z^4 f(x,y,z) = x^2 y^3 z^4 f(x,y,z) = e^x sin(y) ln(z)Homework...

What about the nonlinear forms of it? Or is it guaranteed to reach a global minimum?

Hi all, I need to evaluate the following equation : \mathbf{n} \cdot [\mathbf{\sigma} + \mathbf{a} \nabla\mathbf{\sigma}]\cdot\mathbf{n} where \mathbf{n} is the normal vector, \mathbf{a} a vector, and \sigma the stress tensor such that : \mathbf{\sigma} \cdot \mathbf{n} =...

Homework Statement For the scalar field f(x, y, z) = x2 − y2 − z find gradf and normal unit vector to a surface f(x, y, z) = 0 at the point (1, 1, 0). Homework Equations The Attempt at a Solution I calculated gradf= 2xi -2yj -k at (1,1,0) this is = 2i -2y -k normal unit...

Dear all, Someone could help me to understand how is mathermatically expressed the amplitude of the velocity gradient? For example if vector of velocity is V(Ux,Vy,Wz) The amplitude of the velocity gradient is? : grad(V)= d/dx(Ux) +d/dy(Uy) + d/dz(Uz) Is it fine? Thanks in...

Hi This is a long story, I make it short: I am working in a project where I need to find a matrix defined by a third degree polynomial, the solution can be found iteratively using a gradient descent technique, I am using the golden section line search already implemented in MATLAB (with the...

could someone please help me? what would the divergence, gradient and curl of an oil spill be? I'm a bit confused. Thank you

I looked at my notes, but they're either incomplete or I simply forgot what the professor did to derive the gradient in spherical coordinates. Once I know that, deriving the divergence and curl given the supplementary equations listed is fairly straightforward. It was a little easier but...

Homework Statement A series of true/false questions. I guess I don't understand the concepts of this very well: 1. If you know the directional derivative of f(x,y) in two different directions at a point P, we can find the derivative with respect to the x and y axes and thus we can...

Hello again folks :smile: This thread is regarding the Finite difference scheme for a 1-dimensional Heat transfer problem with non-uniform cross-sectional area. As seen in https://www.physicsforums.com/showthread.php?t=397891", when the element has constant cross-sectional area, things...

Apostol page 386, problem 5 Homework Statement Given f,g continuously differentiable on open connected S in the plane, show \oint_C{f\nabla g\cdot d\alpha}=-\oint_C{g\nabla f\cdot d\alpha} for any piecewise Jordan curve C. Homework Equations 1. Green's Theorem 2. \frac{\partial...

Hello everyone, This might be a bit of a silly question. Just looking at the definition of a gradient of a scalar field in wikipedia: http://en.wikipedia.org/wiki/Gradient" So, the gradient points in the direction of the greatest increase in scalar field. From the definition with the...

I have some measurements from a physics lab experiment and I am coding in Matlab a fit for the data. [Note this is not a problem with Matlab, my problem here is theory] In normal regression of statistics the RMSE is given by: s=\frac{\sigma}{\sqrt{n}} =\sqrt{\frac{\Sigma (\epsilon...

I have been playing around with the Matlab quiver plot, and I found something strange: it seems that the gradient vector isn't computed correctly. ( I use the gradient of an exponential function as a velocity field). Please try the following code. The interesting part is in the last loop...

Homework Statement This is not a homework problem, just a question \nabla(A.B) = (B.\nabla) A +(A.\nabla)B+Bx(\nablaxA)+Ax(\nablaxB) A,B are vectors Homework Equations The Attempt at a Solution I can't make sense of the first 2 terms on the right hand side - is (B.\nabla)...

Homework Statement For every x>-4 where x\in \Re applies sinx+x\leqf(x)\leq8\sqrt{x+4}-16 Find the gradient of the tangent to the curve of f at x_{0}=0 Please help me I am trying to solve this exercise for more than two hours! I'm desperate.

I think I'm having a brain freeze. I'm trying to determine grad f where f(x) = 1/2 xTQx + qTx. I can get to the point where df = (xTQ + qT)dx, but I don't know how to get to the final result grad f = Qx + q. Can someone explain it?

I'm working on a problem where I need to find minimum of a 2D surface. I initially coded up a gradient descent algorithm, and though it works, I had to carefully select a step size (which could be problematic), plus I want it to converge quickly. So, I went through immense pain to derive the...

Hi, I'm having trouble understanding what exactly the gradient of a scalar field represents. According to wikipedia and the textbooks I have it points in the direction of greatest increase and has a magnitude of greatest increase. This by itself seems fine. However, I have also been using it to...

1. Which, if any, has the greater influence on rate of movement down a slope with a constant distance of 80cm: the gradient of the slope or the mass of the object moving down the slope? 2. acceleration = net force / mass 3. If the slope is 90 degrees, the rate of movement of falling...

Homework Statement I am trying to figure out how to take the gradient of a vector function in polar and spherical co-ordinates. Homework Equations The Attempt at a Solution I am aware of how the gradient of a vector function in cartesian co-ords looks, simply the second order...