gradient theorem
If is continuously differentiable function in a simply connected domain (http://planetmath.org/Domain2) of and and lie in this domain, then
(1) |
where the line integral of the left hand side is taken along an arbitrary path in .
The equation (1) is illustrated by the fact that
is the total differential of , and thus
Title | gradient theorem |
---|---|
Canonical name | GradientTheorem |
Date of creation | 2013-03-22 19:11:16 |
Last modified on | 2013-03-22 19:11:16 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Theorem |
Classification | msc 26B12 |
Synonym | fundamental theorem of line integrals |
Related topic | LaminarField |
Related topic | Gradient |