Gradient Definition and 698 Threads

Hi there. I have a doubt that I never cleared before, so I wanted your opinions on this. The thing is that when in vector calculus the gradient vector is presented, one of the "geometric" interpretation that is given is that it's a vector always perpendicular to the curve. So at first I've...

Suppose we have fluid in a vessel (Vessel A) with inside Pressure 120 bar (achieved by a pump)… When we open the valve, the fluid starts to flow into another vessel (vessel B) that was hitherto empty... Due to the Pressure gradient, the fluid flows with a certain velocity into vessel B. But the...

What does it mean to have a taylor expansion of a gradient (vector) about the position x? I.e. taylor expansion of g(x + d) where g is the gradient and d is the small neighborhood.

Homework Statement Let's say \vec{F} = <P,Q,R> If I take the gradient, shouldn't I get \nabla \vec{F} = <\frac{\partial P }{\partial x}, \frac{\partial Q}{\partial y}, \frac{\partial R}{\partial z}> Also why is grad(div f) meaningless? My book says it's because div(f) gives a scalar field...

Hi, could you please help me with my homework? I want to determine the height of mountain (from foot to peak) using the speed of sound. Homework Statement Known data: time delay, height1, temp1 plus known dependence between the height and temperature. What I want to determine: height2...

Homework Statement I am getting quite confused as to the concepts behind this task. I have a function given as a double integral, and am asked to find the gradient of it. However, I have no notes on how to do this, so it is either a very simple task, or the lecturer has once again missed...

i don't really understand the difference :( ∇2V versus ∇ (∇ . V) ? can anyone give me a simple example to showcase the application difference? thanks!

Homework Statement given grad f = xy i + 2xy j+0 k find f(x,y,z) how to generally solve questions of this type Homework Equations The Attempt at a Solution the ans is 0. don't know how.

Homework Statement You are at P(-1,1) on the surface z = (y-x^2)^3. What direction should you move from P so that your height remains the same? Homework Equations The Attempt at a Solution So I basically do not want my height z to change. In this case, I will take a vector...

Hi folks! I was wondering if anyone can help me with a problem I'm having with the concept of thermocouples. If I understand correctly, there should necessarily exist a temperature GRADIENT in one of the conductive couples in order for the emf to be generated. So how can you make sure...

Homework Statement Find delta f of f=Z^-1 * Sqrt(9x^2*y^2) at point (1,4,10) Homework Equations f =f+(fx*delta x )+(fydelta y)+(fz*delta z) The Attempt at a Solution fx = 9*2x/(z*(2*sqrt(9x^2*y^2)) =.18 plugging in (1,4,10) fy=2y/(z*(2*sqrt(9x^2*y^2)) =.08 fz=(sqrt(9x^2*y^2) )...

Hi, Suppose we have a function of two n-dimensional vectors f(\mathbf{x},\mathbf{y}). How can we find the gradient and Hessian of this function? Regards

Hopefully this is a simple enough question. Let (M,g) be a matrix Riemannian manifold and f: M \to \mathbb R a smooth function. Take p \in M and let \{ X_1,\ldots, X_n \} be a local orthonormal frame for a neighbourhood of p. We can define a gradient of f in a neighbourhood of p as \nabla...

Homework Statement Suppose F: Rn --> R has first order partial derivatives and that x in Rn is a local minimizer of F, that is, there exists an r>0 such that f(x+h) \geq f(x) if dist(x, x+h) < r. Prove that \nabla f(x)=0. Homework Equations We want to show that fxi(x) =0 for i = 1,...,n So...

Hello. I hope I've chosen the correct place to post this. Apologies if it is not. Could somebody explain the method of Gradient Descent to me or give me a link to a good explanation? For example, if h(x,y) = x^2 + y^2, what would I do to find a minimum point using gradient descent? I've...

Homework Statement Show that the operation of taking the gradient of a function has the given property. Assume that u and v are differentiable functions of x and y and that a, b are constants. Homework Equations Δ = gradient vector 1) Δ(u/v) = vΔu - uΔv / v^2 2) Δu^n = nu^(n-1)Δu...

Trying to prove that the gradient of a scalar field is symmetric(?) Struggling with the formatting here. Please see the linked image. Thanks. http://i.imgur.com/9ZelT.png

I have a problem with calculating the concentration gradiant. Here is the question and the solution from the solution manual and the numbers don't add up. A 1-mm sheet of FCC iron is used to contain nitrogen in a heat exchanger at 1200℃. The concentration of N at one surface is 0.04 atomic...

For the Scan attachment: The question asks me to find the maximum acceleration. I used those two points in red in the attachment to calculate the gradient doing difference in y and difference in x. I got 4m/s ^2: does it seems correct, or I should have to tangent it? Because it seemed to be a...

Hi, I am curious if anyone here remembers the gradient operator by the following definition: \nabla f = \lim_{\Delta v->0} \frac{1}{\Delta v}\oint f \vec{dS}. So far I could find only one book that gives the definition above. I find this definition quite nice as the expressions of the...

Homework Statement I know that for a general co-ordinate system, the gradient can be expressed as it is at the bottom of this page: http://en.wikipedia.org/wiki/Orthogo...ree_dimensions However, the book I am working from (A First Course in Continuum Mechanics by Gonzalez and Stuart)...

I know that for a general co-ordinate system, the gradient can be expressed as it is at the bottom of this page: http://en.wikipedia.org/wiki/Orthogonal_coordinates#Differential_operators_in_three_dimensions However, the book I am working from (A First Course in Continuum Mechanics by Gonzalez...

Homework Statement hi, any help with proving that grad (v_ . r_) = v_ using spherical polars, where v_ is a uniform vector field would be great it is trivial to prove using summation convention or cartesian coordinates but having to use spherical polars looks messy... thanksHomework Equations...

dot product, and the gradient urgent pls!... Homework Statement Δ<-- this be the gradient and B<-- be a vector B X= xi +yj + zk *<---- be the dot product. (B*Δ)X=B Homework Equations n/a The Attempt at a Solution im not sure how to go about this but this is what i did i...

The adiabatic heat gradient is determined as \gamma = \frac{g}{c_{p}} where \gamma is the rate that temperature falls when rising in an atmosphere. g is gravitational acceleration and c_{p} is the heat apacity. On Earth it is 9.8 Kelvin per kilometer close to the surface of the Earth...

Can you help we are having an all weather football pitch installed and there is a question over the fall for drainage. it states that the fall should not exceed 1% over the total length. my question is what is the maximum fall at 1% if the pitch is 36 metres long please

Difficult gradient problem! Consider the curve with equation x2 + xy + y2 = 3. (a) Find in terms of k, the gradient of the curve at the point (−1, k). (b) Given that the tangent to the curve is parallel to the x-axis at this point, find the value of k.

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.

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?