IEVref: 102-05-19 ID: Language: en Status: Standard Term: gradient Synonym1: Synonym2: Synonym3: Symbol: Definition: vector grad f associated at each point of a given space region with a scalar f, having a direction normal to the surface on which the scalar field has a constant value, in the sense of increasing value of f, and a magnitude equal to the absolute value of the derivative of f with respect to distance in this normal directionNote 1 to entry: The gradient expresses the variation of the scalar field quantity from the given point to a point at an infinitesimal distance $\mathrm{d}s$ in the direction of a given unit vector e by the scalar product df = grad f ⋅ e ds. Note 2 to entry: In orthonormal Cartesian coordinates, the three coordinates of the gradient are: $\frac{\partial \text{\hspace{0.17em}}f}{\partial \text{\hspace{0.17em}}x}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\partial \text{\hspace{0.17em}}f}{\partial \text{\hspace{0.17em}}y}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\partial \text{\hspace{0.17em}}f}{\partial \text{\hspace{0.17em}}z}$. Note 3 to entry: The gradient of the scalar field f is denoted grad f or $\mathbf{\nabla }\text{ }f$. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO 2017-08-24: Order of and tags corrected. LMO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: