Mar 27, 2018 · First up, this question differs from the other ones on this site as I would like to know the isolated meaning of nabla if that makes sense. Meanwhile, other questions might ask …

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 + …

Feb 9, 2019 · you shall take the proper orientation for the vectors (column/row) and the proper convention on how the operator $\nabla$ will apply to vectors on the left or on the right.

Oct 2, 2024 · Don't go from vector algebra to vector calculus identities. This is not a triple product of "regular" vectors, since ∇ is used to write differential operators that can be written as formal …

Jul 21, 2018 · Suppose you have a vector field A =A1i^ +A2j^ +A3k^ A = A 1 i ^ + A 2 j ^ + A 3 k ^. Then ∇ ⋅ A ∇ A would represent the divergence. But what does A ⋅ ∇ A ∇ mean below, and …

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

Aug 23, 2022 · While some identities involving $\nabla$ look very similar to the Leibniz rule, the problem is that $\nabla (X\cdot Y)\neq (\nabla X)Y+X\nabla Y$. (If equality held here, I think a …

12 Is there any clear intuition behind the identity $$ \nabla\times (\nabla\times A)=\nabla (\nabla \cdot A)-\nabla ^2A $$ Though the result is useful and not difficult to derive, it doesn't quite …

This makes clear that the partial derivatives aren't of the basis vectors. In general, $\nabla$ uses a basis of dual (or "cotangent") vectors. For a Cartesian basis, the dual basis vectors are …

Nov 29, 2022 · Note: for line 3 I moved nabla to the front of the first term on the right side of the equation. My professor said it was interesting, but he couldn't approve of my use of del since …