Gradient of a scalar function

Gives the vector of partial derivatives of a scalar function with respect to each Cartesian coordinate, pointing in the direction of steepest increase of the function. It is used throughout vector calculus, physics and engineering to describe how a scalar field changes in space.

\nabla φ = i \sum e_{i} \frac{\partial φ}{\partial x _{i}}

\nabla \varphi = \sum_i \boldsymbol{e}_i \frac{\partial \varphi}{\partial x_i}

What the symbols mean

$\nabla φ$	gradient of the scalar function \varphi, a vector field
$φ$	scalar function (scalar field) of the coordinates
$e_{i}$	Cartesian unit vector along the i-th coordinate axis
$x_{i}$	i-th Cartesian coordinate

About this formula

FieldMathematics
TopicVector calculus
LevelUniversity
Also calledgradient, gradient operator, grad, grad operator, gradient vector, nabla phi
SourceWikidata Q173582

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