Gradient Definition and 698 Threads

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...

Hello, I don't understand the meaning of equation \int\dot{s}_{ij}\frac{\partial v_{j}}{\partial x_{i}} dV where \dot{s} is rate of change of stress, v_{j} is velocity. Can anybody describe the meaning of this equation? Thank you.

It states in course notes: ------------------------------------------- If y = f(x) defines a surface in (n+1) dimensional space then the normal is defined as the (n+1)-dimensional vector: (\frac{\partial f(x)}{\partial x1},(\frac{\partial f(x)}{\partial x2},...,(\frac{\partial f(x)}{\partial...

Homework Statement What is the relationship between electric field strength and the potential gradient? Homework Equations The Attempt at a Solution This is my Calc based Physcis lab question but I am at a total loss. I do not understand what potential gradient is in the...

Hi, I was asked to prove this identity, I found the determinants for both the left and the right side, and now I basically have to prove that (d/dy)(f(dg/dz))=(df/dy)(dg/dz), the d's are actual partials though. Can anyone give me an idea on how to prove this? Thanks.

Homework Statement gradient of the stationary points of y=1-2sinx domain 0<x<2piHomework Equations The Attempt at a Solution dy/dx = -2cosx -2cosx=0...?

Hello everyone! Having a field \bf B = \nabla \times \bf A , how is it possible to get \bf A ? For constant fields, the answer is easy, but is there a general approach to find A ? Some algorithm to do it numerically would help me immensly, too. If anyone knows some book or reference...

I teach marine biology and have been presenting the traditional model of the equilibrium tidal theory (2 humps on rotating earth) as still presented in most basic texts, but have not been able to find the theory or presumed explanation for the apparent generally increasing amplitude in tidal...

Hi, I'm trying to compute the gradient tensor of a vector field and I must say I'm quite confused. In other words I have a vector field which is given in spherical coordinates as: \vec{F}=\begin{bmatrix} 0 \\ \frac{1}{\sin\theta}A \\ -B \end{bmatrix} , with A,B some scalar potentials and I...

We need a MATLAB code for a normalized gradient eq. help! :) Hello, we need help in converting this normalized gradient equation into a MATLAB code. Please see the image. Thanks! :) http://img706.imageshack.us/img706/7998/thesisformula.jpg

Homework Statement There are two parts to this problem. On the curve 2x^2-5 lie two points P and Q. Let the abscissa of P be "x" and the abscissa of Q be "x+h". No numerical coordinates are given. a) State the coordinates of P and Q. b) Using these points find the gradient of...

I'm working on a control theoretical problem and trying to implement the solution in Matlab. Part of the solution requires minimizing a function f(x), for which my predecessor has opted to use a conjugate gradient method. He wrote his own conjugate gradient method, but it's not converging. I've...

I would like to demonstrate an identity with the [SIZE="4"]INDICIAL NOTATION. I have attached my attempt. Please let me know where I made mistakes. Any suggestion? I am trying to understand tensors all by myself because they are the keys in continuum mechanics Thanks

URGENT: Heat transfer - temperature gradient value at a certain point Homework Statement Given a very long cylinder of inner R1 = 0,01 m, outer radius R2 = 0,1 m, that transports water at 150ºC, and surrounded by air at 25ºC, find the temperature gradient value at R = 0,07m. \lambda = 500...

Hello, I just want to confirm with the experts here that I have understood the concept of the gradient correctly. So, a gradient for a function is a vector field that has the partial derivatives of the function. So, for each point in the domain of the function there is a vector associated...

Coulomb gauge fixes gauge by setting div(A)=0. What has it to do with adding a gradient to A and subtract a partial time derivative from V?

In chapter 1 of Sean Carroll's Lecture Notes on General Relativity, p. 12, he writes: In spacetime the simplest example of a dual vector is the gradient of a scalar function, the set of partial derivatives [of the function] with respect to the spacetime coordinates, which we denote by "d"...

Ok hydrogen ion gradient drives ATP synthase. In secondary active transport the preexisting concentration gradient drives the molecules. My question is what do they mean when they say concentration gradient provides energy to do this. Is it the movement of ions like hyrdogen from high to low...

Homework Statement A hiker climbs a mountain whose height is given by z = 1000 - 2x2 - 3y2. When the hiker is at point (1,1,995), she moves on the path of steepest ascent. If she continues to move on this path, show that the projection of this path on the xy-plane is y = x3/2 Homework...

I have to find the gradient of a scalar field, h, at a certain point in a direction given by a vector. I know, \vec{\nabla}h will give me the direction of maximum slope, and its magnitude is the magnitude of the slope, but i don't know where to start in finding the slope in any other...

OK, this is really confusing me. Mostly because i suck at spatial stuff. If the gradient vector at a given point points in the direction in which a function is increasing, then how can it be perpendicular to the tangent plane at that point? If it's perpendicular to the tangent plane...

First of all, I don't have a concrete example for this, but I hope it's not too hard to understand what I'm trying to get at. For a multivariable function of, say, 2 variables x and y, the gradient at a point only depends on the existence of partial x and partial y, right? In other words, if...

Homework Statement show that the pyramids cut off from the first octant by any tangent planes to the surface xyz=1 at points in the first octant must all have the same volume Homework Equations The Attempt at a Solution i don't know how to start this problem. any hints?

I need to compute the normal velocity of an evolving front in two dimensions (x,y). Let's say that I have collected numerous x and y position data as a function of time. If I plot these data on a set of x,y,t coordinate axes and fit a surface through them in a manner analogous to fitting a...

Can anyone help me with the following question? Find the path of the steepest descent along the surface z=x^3 + 3y^2 from the point (1, -2, 13) to (0,0,0) Note: the general solution of the differential equation f ' (t)-kf(t) =0 is f(t) = ce^kt, where c is an arbitary number...