Gradient of a function as a vector field.

A vector field (usually defined by a vector function) is a field in which all points have a vector value (having both magnitude and direction). This is different from a scalar field, where points have only a scalar value (having only magnitude). Applying calculus operations such as integration and differentiation to such a field is the focus of vector calculus. Examples include gradient fields, slope fields, magnetic fields, and velocity fields of fluids.

See also

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