What is gradient?

  • (noun): A graded change in the magnitude of some physical quantity or dimension.
    See also — Additional definitions below


In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase. In simple terms, the variation in space of any quantity can be represented (e.g. graphically) by a slope. The gradient represents the steepness and direction of that slope.

Read more about Gradient.

Some articles on gradient:

Cross Level - Curvature - Cant Gradient
... Cant gradient is the amount by which cant is increased or decreased in a given length of track ... The rate of change of cant is used to determine the suitable cant gradient for a given design speed ... Track twist may also be used to describe cant gradient which may be expressed in percentage of cant change per length unit ...
Sperm Chemotaxis in Mammals - Behavioral Mechanism
... spermatozoa, appear to sense a temporal chemoattractant gradient ... This is because the establishment of a temporal gradient in the absence of spatial gradient, achieved by mixing human spermatozoa with a chemoattractant, results in a ... of these observations it was suggested that the response characteristics observed in temporal gradients also occur in spatial gradients an excitation phase, composed of ...
List Of Formulas In Riemannian Geometry - Gradient, Divergence, Laplace–Beltrami Operator
... The gradient of a function is obtained by raising the index of the differential, whose components are given by The divergence of a vector field with components ...
Surface Gradient
... In vector calculus, the surface gradient is a vector differential operator that is similar to the conventional gradient ... The distinction is that the surface gradient takes effect along a surface ... For a surface in a scalar field, the surface gradient is defined and notated as where is a unit normal to the surface ...
Gradient of A Vector
... In rectangular coordinates, the gradient of a vector f = (f1, f2, f3) is defined by or the Jacobian matrix ... In curvilinear coordinates, the gradient involves Christoffel symbols ...

More definitions of "gradient":

  • (noun): The property possessed by a line or surface that departs from the horizontal.
    Example: "A five-degree gradient"
    Synonyms: slope