Dictionary:Gradient

{{#category_index:G|gradient}} (grā dē ∂nt) 1. The first derivative or rate of change of one variable with respect to another variable, often with respect to distance. For example, the change in gravity, temperature, magnetic susceptibility, or electrical potential with respect to horizontal or vertical distance. Sometimes measured with a gradiometer (q.v.). 2. The operation that finds the gradient from a potential function:

$\mathrm {Gradient~of} ~U=grad~U=\nabla {U}={\frac {\partial {U}}{\partial {x}}}\mathbf {i} +{\frac {\partial {U}}{\partial {y}}}\mathbf {j} +{\frac {\partial {U}}{\partial {z}}}\mathbf {k} ;$

$\nabla$ is the operator del (q.v.). See Figure C-14 for expressions of the gradient in cylindrical and spherical coordinates. 3. A component of the gradient in an arbitrary direction, as the horizontal gradient of the magnetic field. See also tensor gradient.