Gradient Definition and 698 Threads

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...

Does anyone have an idea about a formula relating the refractive index of a medium to the temperature gradient (Generally)?

Homework Statement For the vector field = -yi + xj, find the line integral along the curve C from the origin along the x-axis to the point (6, 0) and then counterclockwise around the circumference of the circle x2 + y2 = 36 to the point (6/sqrt(2), 6/sqrt(2)) . Give an exact answer...

the gradient function is |x|^p-2 x and i need to find the function, which apparently is 1/p |x|^p but i can't figure out how to show this. This is for a bigger problem where the function must be convex. and also p>1 I tried, finding the derivative of 1/p |x|^p , but i don't get the gradient...

[SOLVED] Trajectory using gradient and differential equations Homework Statement A heat-seeking particle is located at the point P on a flat metal plate whose temperature at a point (x, y) is T(x, y). Find parametric equations for the trajectory of the particle if it moves continuously in...

Homework Statement Find an expression involving the function \phi(x_1, x_2, x_3) that has a minimum average value of the square of its gradient within a certain volume V of space. Homework Equations We are studying functionals, though so far it has only been of one variable. We're...

1. (a) Write a formula for the number in terms of the perimeter L and the area A of a circle. (b) Write the differential for your answer in part (a). (c) Suppose that L and A are determined experimentally. Write the resulting relative error in using your answer in part (b). 3...

Hi, I have a convex function F(x,y) that I want to optimize. Since, derivative of F does not closed form, I want to use gradient ascent. The problem is, I have constrains on x and y. I don't know how to incorporate this into gradient search. If there was a closed form, I would use Lagrange...

hi all, Couple of months ago I had an entrance exam wherein this problem appeared. (I hope this is what it was). For a scalar function f\left(x\right)=f\left(x_{1},x_{2},...,x_{n}\right) the gradient is given as \nabla f=\left(\frac {\partial f \left(x\right)} {\partial x_1},\frac...

Hi all, Biologist posting here. We have a thermal gradient that doesn't seem very stable. Right now, our setup is the following: hot water runs through one aluminum bar and cold water runs through another. the two bars are about 25cm apart. There is a thin aluminum plate resting on the...

Homework Statement The point P (1/2, 0) lies on the graph of the curve of y=sin(2x-1) Find the gradient of the tangent to the curve of P Homework Equations ...I don't know The Attempt at a Solution I don't know where to start with this problem

Hi. The book I'm reading says "We define the vector that represents both the magnitude and the direction of the maximum space rate of increase of a scalar as the gradient of that scalar". But how does one know in which direction the maximum increase is?

Homework Statement Given the gradient del = x-hat d/dx + y-hat d/dy + z-hat d/dz in rectangular coordinates, how would you write that in spherical coordinates. I can transform the derivatives into spherical coordinates. But then I need to express the rectangular basis vectors in terms of...

Hi all: I have just met a problem. If say there is a triangle ijk on a manifold, D(i), D(j), D(k) are the geodesic distances from a far point to i,j,k respectively. Then g = [D(i) - D(k); D(j) - D(k)], what does g describe? Does is describe the gradient of the vertex k? If u = Vi-Vk, v =...

Homework Statement I have have a set of data pairs (x, y); (1, a) (2, b) (3, c) (4, d) (5, e) (6, f) (7, g) The least squares regression line for the this set is y=3x-12 Determine the new gradient of this line if the original set of scores has been transformed to; (6, a+3)...

http://www.geocities.com/asdfasdf23135/advcal4.JPG Let f(x,y)=depth. What I've seen in the model solutions is that they used the estimate that the partial dervaitve of f with respect to x evaluate at (0,0) is equal to [f(100,0) - f(0,0)] / 100 = 1/4, & the partial dervaitve of f with...

Homework Statement The gradient of f(x,y) = x^2-x+y is: gradient_f(x,y) = (2x-1 ; 1). To find gradient_f(x,y), I set 2x-1 = 0 and 1 = 0 - so there are no points, where gradient_f(x,y) is zero because of 1 != 0?

The problem The Diagram shows the graph of y=x^3-12x+17 A is the maximum point on the curve C is the minimum point on the curve The curve crosses the y-axis at B For the equation find dy/dx, y=x^3-12x+17 (DONE) Heres the problem find the gradient of the curve at B now what am I supposed to...

In a response by Pervect to another topic, he mentioned a device called a Forward mass detector, named after its inventor Dr. Robert Forward. It's an intersting device with the claim that it can detect small gradients in the curvature of spacetime. I couldn't find any info regarding...

Simple gradient question.. I have a kernel function that determines the influence of each water droplet given a radius r: (10/pi*h^5)*(h-r)^3 The gradient of that is: (-30/pi*h^5)*(h-r)^2 But 'r' is not a vector, its a scalar, its just the distance to the point in question. So how do...

Homework Statement This is from Griffiths' Intro to Electrodynamics. He is discussing the field of a polarized object of dipole moment per unit volume \vec{P} viewed at \vec{r} . He then states: \nabla ' \left( \frac{1}{r} \right) = \frac{ \hat{r}}{r^2} Where \nabla ' denotes...

I need to derive the expression for the gradient operator in spherical coordinates. I know the following R =sqrt(x^2+y^2+z^2) theta, call it %, = arctan sqrt(x^2+y^2)/z phi, arctan (y/x) Using dT/dx= dT/dR*dr/dx+dT/d%*d%/dx+dT/dphi*dphi/dx, do partial derivates... dR/dx =...

Hi, I have a random grid, meaning that each cell consists of a random number. I need to evaluate the gradient. I've tried to apply a basic Euler formula (u_(i+1) - u_(i-1))/2dx but since the values can fluctuate a lot, fluctuations are even stronger for the gradient... I'm thinking...

Hi all, I'm trying to understand someone's PhD thesis on the topic of variational surface evolution and its application in computer vision, and I'm having trouble working out how he evaluates some particular types of expressions involving the gradient. I think it'll be easier if I specify the...

Homework Statement A curve has equation: x^2+2xy-3y^2+16=0 Find the co-ordinates of the points on the curve where dy/dx=0 I think I was able to differentiate it and get the coordinates fine, but I'm wanting to plot the function in Mathematica (5.2) to see if I'm right or not (BTW, I...

Homework Statement suppose that grad of f(x,y,z) is always parallel to the position vector xi+yj+zk. show that f(0,0,a)=f(0,0,-a) for any a. The Attempt at a Solution grad of f= fx(x,y,z)i+fy(x,y,z)j+fz(x,y,z)k ; then gradf (dot) pos.vector = |gradf|*|pos.vector| (since cos(teta)=1 )...