Gradient Definition and 698 Threads

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 [SIZE="3"]ρ[SIZE="1"]v= 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...

"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:

purpose of each of the "operators", divergence, gradient and curl? Hi. Can anybody give me a reasonably simple explanation of what the purpose of each of the "operators", divergence, gradient and curl? (I've been looking but I never found something simple to understand) I know how to evaluate...

If someone could gtive me a general idea about how to approach these problems, I would be very grateful! Our class time was devoted to derivation rather than application. 1) Find the angle between the surfaces defined by r^2=9 and x+y+z^2=1 at the point (2,-2,1). 2) The height of a hill...

I was reading vecctor analysis and got the mathematical formulae for gradient but could not understand its physical meaning. What is the physical meaning of gradient of a scalar ? And of a vector . Also, I wanted to know the physical meanings of Divergence and Curl .

Ok, this may sound a little basic but I can’t think of a way of explaining it other than common sense. I should also say that this is for a Geography assignment so not really physics but hope you guys can give me an insight. I’m trying to explain why the steeper the gradient of a river, the...

how do you calculate the rate of change in a graph?? is it just the gradient??

Ok, this is probably easy...but I'm stuck f(x,y) = y^2 + xy - x^2 +2 find the gradient of the normal to the level curve at the point (3,-2) my answer is -1/root65 , but it's supposed to be 1/8. I did it by finding Fx(x,y) = y-2x and Fy(x,y) = 2y+x then finding the absolute value of the...

How can you derive the gradient of a vector R^3 to R in cylindrical coordinates?

For a radiation problem, i am desperate about the expansion of the following equation: \nabla ( \hat{r} /r^2 \cdot \vec{p}(t_o)) where t_o is the retarded time at the center t_o=t-r/c and \vec{p}(t_o) is the electric dipole moment at t_o actually, it expands to 4 main parts and i am...

how do u find the gradient of y-3x=2 :confused:

what follows is a question I asked myself, the answer I figured out, and the new question that arose as a result. I was thinking about the gradient vector on a 3d surface, and how it shows the direction of the max rate of change at a point. the 2 directions perpendicular to it are tangent to...

I was reading this ebook when I found Coulomb's law: http://www.brokendream.net/xh4/elec.jpg What I'm unsure of is how the gradient function applied to 1/|x-x'| is the same thing as |x-x'|/|x-x'|^3... I know what the gradient function is but I'm totally lost as to how the formula was...

FOr the light dependent reaction, In the textbook it says that the H+ concentration gradient across the thylakoid membrane is maintained by: 1) photolysis 2) transport of electrons from photosystem II along carriers 3) formation of NADPH. I can understand 1) and 3), but I have no idea...

Hi everyone, I now have difficulties in using formula for gradient of tensor. The following is tensor for field strength Fsubscripts_alpha_beta = [ 0 -Ex -Ey -Ez Ex 0 Bz -By Ey -Bz 0 Bx Ez By -Bx 0 ] My question is, how do we derive the Maxwell equations...

Hello, I have to do a proof and am having trouble starting. The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions. Cholesky decom. means I can write the symmetric positive definite matrix as A = GG' The textbook gives a way...

I am not completely satisfied with Griffith's explanation for the geometrical interpretation of a gradient. Can someone elaborate on the geometrical meaning of the magnitude and the direction of a gradient?

What do you see as the best explanations for validity of non-local & gradient constitutive models (considering metal plasticity and damage)? On many occations they naturally work much better than traditional models, but I'm looking for other directly physical phenomena based information, not...

Find the gradient of the curve y=\frac{5x-4}{x^2} at the point where the curve crosses the x-axis. After I differentiating the equation, I got -\frac{5}{x^2} + \frac{8}{x^3} (it might be wrong). Now what do I do?

I'm going to be completely unambiguous on this: the problem I am about to ask is an assigned homework problem so please, do NOT simply just reply with the answer. I have no intention to cheat. That said, the question I have is with regards to problem 12.55 in Griffith's Intro to...

Is there a simple way to calculate or gauge the gradient of a hill?

"partial integration" of gradient vector to find potential field I'm studying out of Stewart's for my Calc IV class, and hit a stumbling block in his section on the fundamental theorem for line integrals. He shows a process of finding a potential function f such that \vec{F} = \nabla f , where...

I'm wondering if physics ever uses a differential equation of the form of a curl of a gradient of a scalar function. Or is this too trivial? Thanks.

Consider the function z=f(x,y). If you start at the point (4,5) and move toward the point (5,6), the direction derivative is sqrt(2). Starting at (4,5) and moving toward (6,6), the directional derivative is sqrt(5). Find gradient f at (4,5). Okay, this is probably a simple problem, but I...

Here's the problem. Find the gradient of f(x,y). f(x,y)=(x^2)e^-2y. I don't have the solution to this and I need to know if I got the right gradient (I have more problems that depend on this gradient, points on it). I ended up getting, gradient f=<2xe^-2y, 2x-2e^-2y>. I don't think it's...