Del Definition and 82 Threads

I electrodynamics, I've seen \nabla ' and \nabla where first is spatial derivative respect to source point and later spatial derivative respect to field point. I am confuse. According to multi-variables calculus, the \nabla operator is spatial derivative of either a scalar or a vector...

Gradient is the derivative of a scalar field. Divergence and Curl are both derivative of a vector field. 1) Are "scalar field" and "vector field" imply it is spatial dependent...ie they are function of any single point in space...ie the value of scalar and vector field is different at every...

Hello all, I am reading a research paper and have found the equation below: http://latex.codecogs.com/gif.latex?\mathbf{z}%20=%20\mathbf{a}%20-%20%28\nabla^2E%28\mathbf{t}%29%29^{-1}\Delta%20E%28\mathbf{t}%29%29 in which E is some function with the variable t being the vector input, and a...

I'm trying to understand how to manipulate equations with del operators. If I have a equation like : div( A + B ) = div(E) and assume A,B,E are twice differential vectors do div cancel? can I say E = A + B? If I write is like this div( A + B - E ) = 0 div( A + B - (A + B)) = 0...

Homework Statement I have to do an E&M problem, I think I got it, but I made a few steps that I don't really understand. The first one is: If delxB= muJ Does del x dB/dt = mu dJ/dt ?? If so, why ? I tried using latex, but it didn't work...sorry :( Homework Equations...

How can you express the del operator after a change of variables? For example, if I want to use cylindrical coordinates for a fluids problem, what is the del operator in terms of the new coordinates? And how do you derive it for any other arbitrary coordinate transforms?

I have several problems like these, I am learning about Levi-Civita and Kroenecker delta so those may be relevant, however, what I am really looking for is further discussion or good books/online tutorials that are specific to usage of the del operator. Homework Statement I'm actually going...

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

hi, I'm trying to follow a derivation in a paper and this equation is confusing me: (u'.\nabla)U = (\nablaU).u' Where U and u' are velocities. The operation of del on the vector U without a dot or cross product is giving me some grief. Can someone explain how this works to me...

I'm an engineering major taking an advanced level physics class. I realize that I really have no clue when it comes to basic mathematics, and it is extremely frustrating. I always just learned *how* to solve equations, never what I was actually doing. For example the del operator. What...

Homework Statement Prove the vector identity: \left(a\times\nabla\right)\bullet\left(u \times v\right)=\left(a \bullet u \right)\left(\nabla \bullet v \right)+\left(v \bullet \nabla \right)\left(a \bullet u \right)-\left(a \bullet v \right)\left(\nabla \bullet u \right)-\left(u...

Homework Statement Write the del operator in spherical coordinates? Homework Equations I wrote the spherical unit vectors: \hat{r}=sin\theta.cos\phi.\hat{x}+sin\theta.sin\phi.\hat{y}+cos\theta.\hat{z} \hat{\phi}=-sin\phi.\hat{x}+cos\phi.\hat{y}...

Can anyone please explain the Del operator. I am much confusesd about it. One formula says that it gives the normal vector to the tangent plane and other tell me that it is gradient of the surface. What it actually is??

Homework Statement prove grad(f/g)=((g grad f)-(f grad g))/g^2,if g not equal to 0. Homework Equations no idea. The Attempt at a Solution rhs will be grad f -(f grad g)/g^2. can't make out what 2 do after that.referred other books but no help.it's a very obscure identity.found...

The gradient, divergence, curl and Laplacian operators are so much a part of classical electromagnetism, I was wondering: what is their history? Who invented them? Newton? Laplace? Maxwell himself?

So given the common explanation here for Del dot B equals 0 to be "There are no magnetic monopoles.", since the title indicates that the equations in a vacuum have the same form, would the meaning of Del dot E = 0 mean that "There are no ELECTRIC monopoles?"...which we assume to be false...

http://img208.imageshack.us/img208/5153/12802868.png Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?

hi all, do you know what is the gradient of a tensor looks like? I mean the del operator on a second order tensor, not the divergence of the tensor. And actually I need them in polar coordinates.. I have been searching so hard in web, but I can't find anything useful. Please help.

Hi, it's not quite a homework question, altought this question came up to mind when i was trying to solve a homework problem. sorry if this shouldn't be here... The thing is this, what are the conditions i should impose to f: R^n -> R in order to be able to find a g, such that [divergence of g...

Homework Statement Not going to write out the whole problem (yet). It's a "find the error in the incorrect proof" type of question in a section on curl and divergence. Homework Equations B = \nablax A is given as an equation of "electromagnetic theory" and used in the proof. It's...

Homework Statement I was reading some notes about the del operator, and they make the statement ∇ x (Ua) = U(∇ x a) + (∇U) x a. However, I disagree with this because it seems to me that in the right hand side of the equation for the second term, the ∇ is operating on a, since a appears...

Homework Statement I would like to transform the Del operator form rectangular coordinate system to spherical coordinate system. The find the Laplace operator in spherical coordinate. 2. The attempt at a solution 1) In rectangular coordinate system, Del operator is given by \nabla =...

hi there! I have some questions concerning the del operator when you use it together with the epsilon tensor and kronecker delta: 1. if you have: phi - scalar, B vector fields \partial_j(\phi B)_i is it equal to: \partial_j(\phi B)_i=(\partial_j\phi)B_i+\phi(\partial_jB_i) or I...

G'day, If you're given a vector q and have that del x p=q (i.e curl(p)=q), how would you find p? Also for divergences. cheers

Hi. Is it true that (\mathbf A\cdot\nabla)\mathbf B=\mathbf A\cdot(\nabla\mathbf B) ? I don't get it. What is the point of writing it like the left hand side?

What does it mean to operate with \frac{d}{\vec{v}} where v is a vector? Say you have another vector q, how do you do \frac{d\vec{v}} {d\vec{q}}[\itex]? What about [itex]\frac{d\vec{v}} {d\vec{v}}? (Can't remember how to do the proper font sorry)

I've been reading up on these three recently, and wondered if anyone could confirm what I think they do. I'm not 100% I understand these. del (\bigtriangleup), when applied to a scalar, creates a vector with that scalar as each of the XYZ values. eg \bigtriangleup . x = (x,x,x)...

hello every one, i am working on vector analysis and i have come across this definition of del operator.i don't understand where does it come from but it works great to determine rotation curl gradient or other stuff of a vector field.can anyone tell me how we are getting this magical operator...

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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...

Hello All, May I know what is the difference between 1) Del operator with respect for field point 2) Del operator with respect to source point thanks newbie

I have been thinking about this for a while, but why is the del operator a vector?? The book i have states no reason why and i was thinking if you guys could tell me why. Thanks...