Gradient Definition and 723 Threads

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...