Difference between revisions of "Nabla"
(Created page with "{{Definition}} ==Definition== <math>\nabla(\ )=\mathbf{i}\frac{\partial(\ )}{\partial x}+\mathbf{j}\frac{\partial(\ )}{\partial y}+\mathbf{k}\frac{\partial(\ )}{\partial z}</...") |
(No difference)
|
Revision as of 23:56, 12 February 2015
Definition
∇( )=i∂( )∂x+j∂( )∂y+k∂( )∂z
Laplace operator
∇⋅∇( )=∇2( )=∂2( )∂x2+∂2( )∂y2+∂2( )∂z2
Notes (other forms seen)
I've seen a book (Vector Analysis and Cartesian Tensors - Third Edition - D E Borune & P C Kendall - which is a good book) distinguise between the ∇s used.
I will use →∇ to denote "bold" ∇, which I usually draw by drawing a triangle, then a line down the left and across the top. I write just ∇ as a triangle with a line down the left side. This works well.
I define →∇n( )=i∂n( )∂xn+j∂n( )∂yn+k∂n( )∂zn and ∇n( )=∂n( )∂xn+∂n( )∂yn+∂n( )∂zn as a slight extension to this notation.
1 book using this doesn't mean that the other books are wrong, it could be on to something. However in practice I have never actually come across the need for this. Which is why I list the first two definitions. I write this to show I have considered alternatives and why I do not use them.