Jun 25, 2019 · @VinayVarahabhotla $\nabla F$ and $\nabla^2F=\nabla\cdot\nabla F$ can be given a meaning using ideas from differential geometry, but it is probably a little too advance for you now.

Mathematicians i know refer in general to the differential operator represented by the symbol ∇ ∇ (nabla) as del. Like someone refers to the operator of addition, represented by the symbol of + with the word …

Mar 27, 2018 · The nabla can be applied to a number of different areas in multivariable calculus, such as divergence or curl. In all these cases, the nabla can be treated like a vector which you can dot or …

The following passage has been extracted from the book "Mathematical methods for Physicists": A key idea of the present chapter is that a quantity that is properly called a vector must have the

Feb 9, 2019 · The nabla vector operates on something, changing what it was into something new. Also, the higher dimensions of a a, the more careful we will need to be with our notation.

Jul 21, 2018 · Looking at the coordinate-free expressions that you've found in Wikipedia, it is easy to convince yourself that grad g r a d, curl c u r l, and div d i v are instances of the exterior derivative in …

Oct 17, 2019 · There are several very important vector identities involving $\\nabla$ that I struggle to understand. To give an example, in the derivation of the wave equation from maxwell's equations, …

Apr 27, 2015 · The notation ⋅E → E → is taking a bit of a liberty with the mathematical 'del' operator and the dot product operation. As you probably know, the dot product of two vectors is defined by: a = …

where A A and B B are vectors. What's the definition of this? I've also seen this in some identities

The problem I have is with the step $\nabla \times \vec {v} = \vec {0}$, i.e. $\nabla \times \vec {J} = \vec {0}$. My main text discards the respective term without any comment and another derivation I looked …