Gradient vs. Nabla — What's the Difference?

(Mathematics) A vector having coordinate components that are the partial derivatives of a function with respect to its variables.

A Hebrew stringed instrument.

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} is the vector whose components are the partial derivatives of f {\displaystyle f} at p {\displaystyle p} . That is, for f : R n → R {\displaystyle f\colon \mathbb {R} ^{n}\to \mathbb {R} } , its gradient ∇ f : R n → R n {\displaystyle \nabla f\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}} is defined at the point p = ( x 1 , … , x n ) {\displaystyle p=(x_{1},\ldots ,x_{n})} in n-dimensional space as the vector: ∇ f ( p ) = [ ∂ f ∂ x 1 ( p ) ⋮ ∂ f ∂ x n ( p ) ] .

(analysis) The symbol ∇, used to denote the gradient operator.

A rate of inclination; a slope.

An ascending or descending part; an incline.

(Physics) The rate at which a physical quantity, such as temperature or pressure, changes in response to changes in a given variable, especially distance.

(Biology) A series of progressively increasing or decreasing differences in the growth rate, metabolism, or physiological activity of a cell, organ, or organism.

A slope or incline.

A rate of inclination or declination of a slope.

The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.

(science) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.

A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ

A gradual change in color. A color gradient; gradation.

Moving by steps; walking.

Rising or descending by regular degrees of inclination.

Adapted for walking, as the feet of certain birds.

Moving by steps; walking; as, gradient automata.

Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.

Adapted for walking, as the feet of certain birds.

The rate of regular or graded ascent or descent in a road; grade.

A part of a road which slopes upward or downward; a portion of a way not level; a grade.

The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.

The variation of the concentration of a chemical substance in solution through some linear path; also called concentration gradient; - usually measured in concentration units per unit distance. Concentration gradients are created naturally, e.g. by the diffusion of a substance from a point of high concentration toward regions of lower concentration within a body of liquid; in laboratory techniques they may be made artificially.

A graded change in the magnitude of some physical quantity or dimension

The property possessed by a line or surface that departs from the horizontal;