Gradient Definition and 723 Threads

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 )...

Homework Statement Find the angle between (grad)u and (grad)v at all points with x!=0 and y!= 0 if x =( e^u)*(cos v) and y = (e^u) (sinv) . The Attempt at a Solution is not here x and y a function of u and v? How are we going to find grad of u and v? Should we pull out u and y from...

Hi , I need help about procedure on this problem: Consider a sphere of charge density ρv= 2/r[C/m3] having a radius a (no charge outside), centered at the origin. Perform the following steps: a) Calculate the electric field both inside and outside the sphere using Gauss’ law. b) Calculate...

"You are standing at the point (30, 20, 5) on a hill with the shape of the surface z=100exp((-x^2+3y^2)/701). In what direction should you proceed in order to climb most steeply?" SInce the grad vector allegedly points in the most steep direction of the surface, I guess I'll have to compute...

What is the gradient vector, really? My textbook both states that it is a vector normal to a certain point on a surface, but also that it is a vector that points in the direction with the maximum slope of a surface. I find this slightly ambiguous.

Homework Statement Find the directional derivative of f=sqrt(xyz) at P(2,-1,-2) in the direction of v=i+2j-2k The Attempt at a Solution I calculate the gradient vector and obtain grad(f) at P= <1/2, 1, 1/2> Then I find the unit vector of v, which is <1/3, 2/3, -2/3> The...

Sorry to ask yet another question, but it's very hard to contact my teacher. Homework Statement f(x,y,z) = x^2-yz+z^2 a = (0,1,1), b = (1,3,2). Find a point c on the line joining a and b such that; f(b)-f(a)=\nabla f(c)\bullet(b-a) 2. The attempt at a solution f(b) =...

I want to find the gradient vector of f(x,y,z)=2*sqrt(xyz) at the point ((3,-4,-3). I find the partials and set in for the x-, y-, and z-values, and find the grad. vector (2, (1,5), 2). The right solution is (2, (-1,5), -2), so I have obviously made a mistake with the sqrt. How do I know...

I'm wondering if there are any convenient symbolic "shortcuts" (i.e. abuse of notation) that enable one to compute the gradient with respect to a certain vector, without decomposing the computation into the vector's individual elements and differentiating with respect to each element. For...

when u=-0.6i+0.8j, Du f(1,2)=? gradient f=(18,9) I use unit vector dot (-0.6,0.8) dotted with the gradient f, which turns out to be -3.6 so here is the question. A: the maximum value of Dv f(1,2) is=? B: this maximum occurs when v=(?,?) I'm confued with the Dv thing. For my guess is that I...

Is there a direction A in which the rate of change of the temperature function T(x,y,x)=2xy - yz at P(1,-1,1) is -3ºC/ft? Give reasons for your answer. For this problem I found the gradient of at the point P. So \nabla f = 2y|_p \mathbf{i} + 2x-z|_p \mathbf{j} - y|_p \mathbf{k} which I...

Hi, can someone please explain to me what is meant by a temperature gradient in the context of thermodynamics? Something I've been reading goes along the lines of "...To reverse the direction of conduction would require a reversal of the temperature gradient in the conductor. Thermal conduction...

Dear All, I have a signal, which is a time series from measuring some quantity. The trend of the signal is decreasing. However, due to noise, the signal is fluctuating. Is there some method to get a good estimation of the gradient of the signal, i.e. the average reduction of the quantity...

Hello, The latest research of mine concerning the derivative of a function without using diffrentiation and even without having the knowledge of what the equation of the funtion is, is attached to the post, please send me your comments on this latest document of mine. With regards. Mubashir

I was wondering if anyone could help me with this rather arbitrary math problem. I need a description of what a gradient is in mostly non-math terms. I know a gradient is a sort of slope, but I don't understand where you would draw the line of what is and what is not a gradient. Meaning which...

If we define the Gradient of a function: \uparrow u= Gra(f) wich is a vector then what would be the covariant derivative: \nabla _{u}u where the vector u has been defined above...i know the covariant derivative is a vector but i don,t know well how to calculate it...thank you.

Gradient, divegrance and curl? del operator! in static magnetic and electric fields, the del operator was introduced and then used to describe three different quantities.. i still can't quite figure out the physical meaning and difference between the curl,divergance and the gradient in terms of...

now, this is a rather basic question, but, i can't seem to find the answer... so anyhow, i always thought that a gradient diddent need units and was just used to compare the change between two things, but i think i may be wrong. so, if you are plotting extension (m) over force (n) for a...

How can the electric polarization be induced by the strain gradient? It is said in some papers the strain gradient can induce electric polarization in solid materials. Why can it happen? Who can explain this phenomenon to me?

Is it always true that the gradient of a function is normal to the flux coming out of the surface represented by the function?

Let f : Rn -> R. Suppose that grad(f(x)) = 0 for all x in some open ball B(a, r). Show that f is constant on B(a, r). [Hint: use part (a) to make this a problem about a function of one variable] part (a) is show that for any two points x, y in B there is a straight line starting at x...

Suppose distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which is the origin. The temperature 1 lightyear from the origin is 100 degrees celsius. Find the gradient of T at (x,y,z). here's what I...

One last question for tonight... If you let f: R^n ---> R (Euclidean n-space to real numbers) and f(x) = ||x-a|| for some fixed a, how would you define the gradient in terms of symbols and numbers (not words)?

The gradient of the curve C is given by: dy/dx = (3x-1)2 the point P (1,4) lies on C. a) Find an equation of the normal to C at P. b) Find an equation for the curve C in the form y=f(x) c) using dy/dx = (3x-1)2 show that there is no point on C at which the tangent is parallel to the line...

Hi please , can someone help me with this problem. I need to know the procedure. Let f(x,y)=x^3-xy. set a(0,1) and b(1,3). Find a point c on the line sement[ab] for which f(b)-f[a]= gradient(f[c]) * (b-a) Thank you B.

If we plot velocity in ms-1 over time in seconds, the gradient of the curve is acceleration or ms-2. If we plot time squared i.e. s x s over distance in metres, what are the units of the gradient? :redface: